Relevant bibliographies by topics / Quantum superalgebras

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Quantum superalgebras'

Author: Grafiati
Published: 4 June 2021
Last updated: 13 February 2022

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Journal articles on the topic "Quantum superalgebras"

1

RASMUSSEN, JØRGEN. "SCREENING CURRENT REPRESENTATION OF QUANTUM SUPERALGEBRAS." Modern Physics Letters A 13, no. 18 (June 14, 1998): 1485–93. http://dx.doi.org/10.1142/s021773239800156x.

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In this letter a screening current or contour representation is given for certain quantum superalgebras. The Gomez–Sierra construction of quantum groups in conformal field theory is generalized to cover superalgebras and illustrated using recent results on screening currents in affine current superalgebra.
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DU, JIE, and JINKUI WAN. "THE QUEER -SCHUR SUPERALGEBRA." Journal of the Australian Mathematical Society 105, no. 3 (February 2, 2018): 316–46. http://dx.doi.org/10.1017/s1446788717000337.

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As a natural generalisation of $q$-Schur algebras associated with the Hecke algebra ${\mathcal{H}}_{r,R}$ (of the symmetric group), we introduce the queer $q$-Schur superalgebra associated with the Hecke–Clifford superalgebra ${\mathcal{H}}_{r,R}^{\mathsf{c}}$, which, by definition, is the endomorphism algebra of the induced ${\mathcal{H}}_{r,R}^{\mathsf{c}}$-module from certain $q$-permutation modules over ${\mathcal{H}}_{r,R}$. We will describe certain integral bases for these superalgebras in terms of matrices and will establish the base-change property for them. We will also identify the queer $q$-Schur superalgebras with the quantum queer Schur superalgebras investigated in the context of quantum queer supergroups and provide a constructible classification of their simple polynomial representations over a certain extension of the field $\mathbb{C}(\mathbf{v})$ of complex rational functions.
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DELIUS, GUSTAV W., MARK D. GOULD, JON R. LINKS, and YAO-ZHONG ZHANG. "ON TYPE I QUANTUM AFFINE SUPERALGEBRAS." International Journal of Modern Physics A 10, no. 23 (September 20, 1995): 3259–81. http://dx.doi.org/10.1142/s0217751x95001571.

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The type I simple Lie superalgebras are sl(m|n) and osp(2|2n). We study the quantum deformations of their untwisted affine extensions Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We identify additional relations between the simple generators (“extra q Serre relations”) which need to be imposed in order to properly define Uq[sl(m|n)(1)] and Uq[osp(2|2n)(1)]. We present a general technique for deriving the spectral-parameter-dependent R matrices from quantum affine superalgebras. We determine the R matrices for the type I affine superalgebra Uq[sl(m|n)(1)] in various representations, thereby deriving new solutions of the spectral-parameter-dependent Yang-Baxter equation. In particular, because this algebra possesses one-parameter families of finite-dimensional irreps, we are able to construct R matrices depending on two additional spectral-parameter-like parameters, providing generalizations of the free fermion model.
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GOULD, MARK D., and YAO-ZHONG ZHANG. "R-MATRICES AND THE TENSOR PRODUCT GRAPH METHOD." International Journal of Modern Physics B 16, no. 14n15 (June 20, 2002): 2145–51. http://dx.doi.org/10.1142/s0217979202011901.

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A systematic method for constructing trigonometric R-matrices corresponding to the (multiplicity-free) tensor product of any two affinizable representations of a quantum algebra or superalgebra has been developed by the Brisbane group and its collaborators. This method has been referred to as the Tensor Product Graph Method. Here we describe applications of this method to untwisted and twisted quantum affine superalgebras.
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ITO, KATSUSHI. "QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA." International Journal of Modern Physics A 07, no. 20 (August 10, 1992): 4885–98. http://dx.doi.org/10.1142/s0217751x92002210.

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We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.
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BOROWIEC, A., J. LUKIERSKI, and V. N. TOLSTOY. "BASIC TWIST QUANTIZATION OF osp(1|2) AND κ-DEFORMATION OF D = 1 SUPERCONFORMAL MECHANICS." Modern Physics Letters A 18, no. 17 (June 7, 2003): 1157–69. http://dx.doi.org/10.1142/s021773230301096x.

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The twisting function describing a nonstandard (super-Jordanian) quantum deformation of osp (1|2) is given in explicit closed form. The quantum coproducts and universal R-matrix are presented. The non-uniqueness of the twisting function as well as two real forms of the deformed osp (1|2) superalgebras are considered. One real quantum osp (1|2) superalgebra is interpreted as describing the κ-deformation of D = 1, N = 1 superconformal algebra, which can be applied as a symmetry algebra of N = 1 superconformal mechanics.
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HEIDENREICH, WOLFGANG, and JERZY LUKIERSKI. "QUANTIZED SUPERTWISTORS, HIGHER SPIN SUPERALGEBRAS AND SUPERSINGLETONS." Modern Physics Letters A 05, no. 06 (March 10, 1990): 439–51. http://dx.doi.org/10.1142/s0217732390000512.

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We introduce supertwistors in D=3 and D=4 as describing the canonical coordinates in two models of fundamental phase space with respectively OSP(N; 4) and u(2, 2; N) invariant fundamental Poisson brackets. The infinite superalgebra of normally ordered polynomials in quantized supertwistor variables can be identified with recently proposed D=3 and D=4 higher spin superalgebras. We consider the supersingleton representations of OSP(N, 4), and OSP(2N, 8) as describing fundamental realizations of D=3 and D=4 supertwistor quantum mechanics.
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耿, 亚娜. "Coordinate Superalgebras of Quantum Superalgebras Based on the RTT Relation." Pure Mathematics 10, no. 12 (2020): 1213–19. http://dx.doi.org/10.12677/pm.2020.1012144.

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Zhang, Huafeng. "Representations of quantum affine superalgebras." Mathematische Zeitschrift 278, no. 3-4 (June 10, 2014): 663–703. http://dx.doi.org/10.1007/s00209-014-1330-6.

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Kac, Victor, Shi-Shyr Roan, and Minoru Wakimoto. "Quantum Reduction for Affine Superalgebras." Communications in Mathematical Physics 241, no. 2-3 (September 12, 2003): 307–42. http://dx.doi.org/10.1007/s00220-003-0926-1.

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Dissertations / Theses on the topic "Quantum superalgebras"

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Blumen, Sacha Carl. "Quantum Superalgebras at Roots of Unity and Topological Invariants of Three-manifolds." University of Sydney. School of Mathematics and Statistics, 2005. http://hdl.handle.net/2123/715.

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The general method of Reshetikhin and Turaev is followed to develop topological invariants of closed, connected, orientable 3-manifolds from a new class of algebras called pseudomodular Hopf algebras. Pseudo-modular Hopf algebras are a class of Z_2-graded ribbon Hopf algebras that generalise the concept of a modular Hopf algebra. The quantum superalgebra Uq(osp(1|2n)) over C is considered with q a primitive Nth root of unity for all integers N > = 3. For such a q, a certain left ideal I of U_q(osp(1|2n)) is also a two-sided Hopf ideal, and the quotient algebra U^(N)_q(osp(1|2n)) = U_q(osp(1|2n))/I is a Z_2-graded ribbon Hopf algebra. For all n and all N > = 3, a finite collection of finite dimensional representations of U^(N)_q(osp(1|2n)) is defined. Each such representation of U^(N)_q(osp(1|2n)) is labelled by an integral dominant weight belonging to the truncated dominant Weyl chamber. Properties of these representations are considered: the quantum superdimension of each representation is calculated, each representation is shown to be self-dual, and more importantly, the decomposition of the tensor product of an arbitrary number of such representations is obtained for even N. It is proved that the quotient algebra U(N)^q_(osp(1|2n)), together with the set of finite dimensional representations discussed above, form a pseudo-modular Hopf algebra when N > = 6 is twice an odd number. Using this pseudo-modular Hopf algebra, we construct a topological invariant of 3-manifolds. This invariant is shown to be different to the topological invariants of 3-manifolds arising from quantum so(2n+1) at roots of unity.
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Grant, Jonathan William. "Diagrammatics for representation categories of quantum Lie superalgebras from skew Howe duality and categorification via foams." Thesis, Durham University, 2016. http://etheses.dur.ac.uk/11618/.

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In this thesis we generalise quantum skew Howe duality to Lie superalgebras in type A, and show how this gives a categorification of certain representation categories of $\mathfrak{gl}(m|n)$. In particular, we use skew Howe duality to describe a category of representations generated monoidally by the exterior powers of the fundamental representation. This description is in terms of MOY diagrams, with one additional local relation on $n+1$ strands. This generalises the $n=0$ case from Cautis, Kamnitzer and Morrison. Using this, we give a categorification of this category in terms of foams, which generalises that of Queffelec, Rose and Lauda in the case $n=0$. The Reshetikhin-Turaev procedure gives a knot polynomial associated to $\mathfrak{gl}(m|n)$, which is a specialisation of the HOMFLY polynomial $P(a,q)$ at $a=q^{m-n}$. For the case $n=0$, the polynomial can be described nicely in terms of MOY diagrams, and therefore is related strongly to skew Howe duality. This was used by Queffelec and Rose to define $\mathfrak{sl}(n)$ Khovanov-Rozansky homology by categorified skew Howe duality. For general $n$, the relationship is less nice, and skew Howe duality is not sufficient to describe a homology theory associated with $\mathfrak{gl}(m|n)$ from our approach. Part of the problem is that the representation category no longer contains duals of the fundamental representations, which means that although a braid has an image in this categorified representation category, it is not possible to close this braid in the same way that Queffelec and Rose do. However, the categorified representation category does give partial progress towards the problem of defining a quantum categorification of the Alexander polynomial.
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Ha, Ngoc-Phu. "Théorie quantique des champs topologiques pour la superalgèbre de Lie sl(2/1)." Thesis, Lorient, 2018. http://www.theses.fr/2018LORIS505/document.

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Ce texte étudie le groupe quantique Uξ sl(2|1) associé à la superalgèbre de Lie sl(2|1) et une catégorie de ses représentations de dimension finie. L'objectif est de construire des invariants topologiques de 3-variétés en utilisant la notion de trace modifiée. D'abord nous prouvons que la H catégorie CH des modules de poids nilpotents sur Uξ sl(2|1) est enrubannée et qu'il existe une trace modifiée sur son idéal des modules projectifs. De plus CH possède une structure relativement G-prémodulaire ce qui est une condition suffisante pour construire un invariant de 3-variétés à la Costantino-Geer-Patureau. Cet invariant est le cœur d'une 1+1+1-TQFT (Topological Quantum Field Theory). D'autre part Hennings a proposé à partir d'une algèbre de Hopf de dimension finie une construction d’invariants qui dispense de considérer la catégorie de H l l ses représentations. Nous montrons que le groupe quantique déroulé Uξ sl(2|1)/(e1 , f1 ) possède une complétion qui est une algèbre de Hopf enrubannée topologique. Nous construisons un invariant de 3-variétés à la Hennings en utilisant cette structure algébrique, une transformation de Fourier discrète et la notion de G-intégrales. L'intégrale dans une algèbre de Hopf est centrale dans la construction de Hennings. La notion de trace modifiée dans une catégorie s'est récemment révélée être une généralisation des intégrales dans les algèbres de Hopf de dimension finie. Dans un contexte plus général d'algèbre de Hopf de dimension infinie nous prouvons la relation formulée entre la trace modifiée et la G -intégrale
This text studies the quantum group Uξ sl(2|1) associated with the Lie superalgebra sl(2|1) and a category of finite dimensional representations. The aim is to construct the topological invariants of 3-manifolds using the notion of modified trace. We first prove that the category CH of the nilpotent weight modules over Uξ sl(2|1) is ribbon and that there exists a modified trace on its ideal of projective modules. Furthermore, CH possesses a relative G-premodular structure which is a sufficient condition to construct an invariant of 3-manifolds of Costantino-Geer-Patureau type. This invariant is the heart of a 1+1+1-TQFT (Topological Quantum Field Theory). Next Hennings proposed from a finite dimensional Hopf algebra, a construction of invariants which does not require to consider the category of its representations. We show that the unrolled H l l quantum group Uξ sl(2|1)/(e1 , f1 ) has a completion which is a topological ribbon Hopf algebra. We construct an invariant of 3-manifolds of Hennings type using this algebraic structure, a discrete Fourier transform, and the notion of G-integrals. The integral in a Hopf algebra is central in the construction of Hennings. The notion of modified trace in a category has recently been revealed to be a generalization of the integrals in a finite dimensional Hopf algebra. In a more general context of infinite dimensional Hopf algebras we prove the relation formulated between the modified trace and the G-integral
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Pepiciello, Martina. "Supersymmetric quantum mechanics and applications." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18379/.

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La tesi contiene un'introduzione alla Meccanica Quantistica Supersimmetrica e alle sue possibili applicazioni nella risoluzione di problemi tipici della Meccanica Quantistica. Dopo una breve discussione sulle origini della Meccanica Quantistica Supersimmetrica, vengono introdotte le superalgebre di Lie, che costituiscono l'apparato matematico necessario per lo sviluppo di questo argomento. Viene poi implementato e studiato il modello con N=2 cariche di supersimmetria in 0+1 dimensioni, affrontando anche il concetto di rottura spontanea di supersimmetria e l'indice di Witten. In seguito, vengono discusse alcune applicazioni di questo modello, ovvero la catena di Hamiltoniane, i potenziali invarianti in forma e la costruzione di una famiglia di potenziali isospettrali. La tesi si conclude con esempi espliciti di tali applicazioni, in cui i metodi della Meccanica Quantistica Supersimmetrica vengono usati per risolvere alcuni problemi unidimensionali.
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(8766687), Luan Pereira Bezerra. "Quantum Toroidal Superalgebras." Thesis, 2020.

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We introduce the quantum toroidal superalgebra Em|n associated with the Lie superalgebra glm|n and initiate its study. For each choice of parity "s" of glm|n, a corresponding quantum toroidal superalgebra Es is defined.

To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed.

The superalgebra Es contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂m|n with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of Es, which exchanges the vertical and horizontal subalgebras.

If m and n are different and "s" is standard, we give a construction of level 1 Em|n-modules through vertex operators. We also construct an evaluation map from Em|n(q1,q2,q3) to the quantum affine algebra Uq gl̂m|n at level c=q3(m-n)/2.
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Pereira, Bezerra Luan. "Quantum Toroidal Superalgebras." Thesis, 2020. http://hdl.handle.net/1805/22682.

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Indiana University-Purdue University Indianapolis (IUPUI)
We introduce the quantum toroidal superalgebra E(m|n) associated with the Lie superalgebra gl(m|n) and initiate its study. For each choice of parity "s" of gl(m|n), a corresponding quantum toroidal superalgebra E(s) is defined. To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of E(s), which exchanges the vertical and horizontal subalgebras. If m and n are different and "s" is standard, we give a construction of level 1 E(m|n)-modules through vertex operators. We also construct an evaluation map from E(m|n)(q1,q2,q3) to the quantum affine algebra Uq gl̂(m|n) at level c=q3^(m-n)/2.
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Zaimi, Meri. "Algèbres de Temperley-Lieb, Birman-Murakami-Wenzl et Askey-Wilson, et autres centralisateurs de U_q(sl_2)." Thesis, 2020. http://hdl.handle.net/1866/24381.

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Mémoire par articles.
Ce mémoire contient trois articles reliés par l'idée sous-jacente d'une généralisation de la dualité de Schur-Weyl. L'objectif principal est d'obtenir une description algébrique du centralisateur de l'image de l'action diagonale de U_q(sl_2) dans le produit tensoriel de trois représentations irréductibles, lorsque q n'est pas une racine de l'unité. La relation entre une algèbre de Askey-Wilson étendue AW(3) et ce centralisateur est examinée à cet effet. Dans le premier article, les éléments du centralisateur de l'action de U_q(sl_2) dans son produit tensoriel triple sont définis à l'aide de la matrice R universelle de U_q(sl_2). Il est montré que ces éléments respectent les relations définissantes de AW(3). Dans le deuxième article, la matrice R universelle de la superalgèbre de Lie osp(1|2) est utilisée de manière similaire avec l'algèbre de Bannai-Ito BI(3). Dans ce cas, le formalisme de la matrice R permet de définir l'algèbre de Bannai-Ito de rang supérieur BI(n) comme le centralisateur de l'action de osp(1|2) dans son produit tensoriel n-fois. Le troisième article propose une conjecture qui établit un isomorphisme entre un quotient de AW(3) et le centralisateur de l'image de l'action diagonale de U_q(sl_2) dans le produit tensoriel de trois représentations irréductibles quelconques. La conjecture est prouvée pour plusieurs cas, et les algèbres de Temperley-Lieb, Birman-Murakami-Wenzl et Temperley-Lieb à une frontière sont retrouvées comme quotients de l'algèbre de Askey-Wilson.
This master thesis contains three articles related by the underlying idea of a generalization of the Schur-Weyl duality. The main objective is to obtain an algebraic description of the centralizer of the image of the diagonal action of U_q(sl_2) in the tensor product of three irreducible representations, when q is not a root of unity. The connection between a centrally extended Askey-Wilson algebra AW(3) and this centralizer is examined for this purpose. In the first article, the elements of the centralizer of the action of U_q(sl_2) in its threefold tensor product are defined with the help of the universal R-matrix of U_q(sl_2). These elements are shown to satisfy the defining relations of AW(3). In the second article, the universal R-matrix of the Lie superalgebra osp(1|2) is used in a similar fashion with the Bannai-Ito algebra BI(3). In this case, the formalism of the R-matrix allows to define the higher rank Bannai-Ito algebra BI(n) as the centralizer of the action of osp(1|2) in its n-fold tensor product. The third article proposes a conjecture that establishes an isomorphism between a quotient of AW(3) and the centralizer of the image of the diagonal action of U_q(sl_2) in the tensor product of any three irreducible representations. The conjecture is proved for several cases, and the Temperley-Lieb, Birman-Murakami-Wenzl and one-boundary Temperley-Lieb algebras are recovered as quotients of the Askey-Wilson algebra.
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Books on the topic "Quantum superalgebras"

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Quantum stochastic calculus and representations of Lie superalgebras. Berlin: Springer, 1998.

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Eyre, Timothy M. W. Quantum Stochastic Calculus and Representations of Lie Superalgebras. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096850.

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Xu, Xiaoping. Introduction to Vertex Operator Superalgebras and Their Modules. Dordrecht: Springer Netherlands, 1998.

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S, Kleshchëv A., ed. Representations of shifted Yangians and finite W-algebras. Providence, R.I: American Mathematical Society, 2008.

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1944-, Kulish P. P., Manojlovic Nenad 1962-, and Samtleben Henning, eds. Infinite dimensional algebras and quantum integrable systems. Basel: Birkhäuser Verlag, 2005.

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1959-, Ariki Susumu, ed. Algebraic groups and quantum groups: International Conference on Representation Theory of Algebraic Groups and Quantum Groups, August 2-6, 2010, Nagoya University, Nagoya, Japan. Providence, R.I: American Mathematical Society, 2012.

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Misra, Kailash C., Milen Yakimov, Pramod N. Achar, and Dijana Jakelic. Recent advances in representation theory, quantum groups, algebraic geometry, and related topics: AMS special sessions on geometric and algebraic aspects of representation theory and quantum groups, and noncommutative algebraic geometry, October 13-14, 2012, Tulane University, New Orleans, Louisiana. Providence, Rhode Island: American Mathematical Society, 2014.

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author, Winternitz Pavel, ed. Classification and identification of Lie algebras. Providence, Rhode Island: American Mathematical Society, 2014.

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Lie algebras, lie superalgebras, vertex algebras, and related topics: Southeastern Lie Theory Workshop Series 2012-2014 : Categorification of Quantum Groups and Representation Theory, April 21-22, 2012, North Carolina State University : Lie Algebras, Vertex Algebras, Integrable Systems and Applications, December 16-18, 2012, College of Charleston : Noncommutative Algebraic Geometry and Representation Theory, May 10-12, 2013, Louisiana State Vniversity : Representation Theory of Lie Algebras and Lie Superalgebras, May 16-17, 2014, University of Georgia. Providence, Rhode Island: American Mathematical Society, 2016.

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Neher, Erhard. Geometric representation theory and extended affine Lie algebras. Providence, R.I: American Mathematical Society, 2011.

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Book chapters on the topic "Quantum superalgebras"

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Kulish, P. P. "Quantum Lie Superalgebras and Supergroups." In Research Reports in Physics, 14–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/978-3-642-84000-5_2.

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Eyre, Timothy M. W. "Quantum stochastic calculus." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 7–21. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096852.

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Eyre, Timothy M. W. "The Ito superalgebra." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 59–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096856.

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Eyre, Timothy M. W. "Some results in Z2-graded quantum stochastic calculus." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 77–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096857.

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Eyre, Timothy M. W. "Representations of lie superalgebras in Z2-graded quantum stochastic calculus." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 33–50. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096854.

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Eyre, Timothy M. W. "Introduction." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096851.

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Eyre, Timothy M. W. "Z2-graded structures." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 23–31. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096853.

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Eyre, Timothy M. W. "The ungraded higher order Ito product formula." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 51–57. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096855.

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Eyre, Timothy M. W. "Chaotic expansions." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 101–12. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096858.

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Eyre, Timothy M. W. "Extensions." In Quantum Stochastic Calculus and Representations of Lie Superalgebras, 113–32. Berlin, Heidelberg: Springer Berlin Heidelberg, 1998. http://dx.doi.org/10.1007/bfb0096859.

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Conference papers on the topic "Quantum superalgebras"

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Tolstoy, V. N. "Multiparameter Quantum Deformations of Jordanian Type for Lie Superalgebras." In Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812772527_0041.

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Ferrara, Sergio. "Superspace Representations of SU(2,2/N) Superalgebras and Multiplet Shortening." In Quantum aspects of gauge theories, supersymmetry and unification. Trieste, Italy: Sissa Medialab, 2000. http://dx.doi.org/10.22323/1.004.0016.

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BURDíK, Č., and O. NAVRÁTIL. "THE Q–BOSON–FERMION REALIZATION OF THE QUANTUM SUPERALGEBRA UQ (GL(M/N))." In Proceedings of the Fifth International Workshop. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702562_0027.

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Uvarov, D. V. "Quantum BRST Charge and OSp(1∣8) Superalgebra of Twistor-Like p-branes with Exotic Supersymmetry and Weyl Symmetry." In FUNDAMENTAL INTERACTIONS AND TWISTOR-LIKE METHODS: XIX Max Born Symposium. AIP, 2005. http://dx.doi.org/10.1063/1.1923336.

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