Journal articles on the topic 'Exterior algebra'

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1

Marchuk, N. "Generalized Exterior Algebras." Ukrainian Journal of Physics 57, no. 4 (April 30, 2012): 422. http://dx.doi.org/10.15407/ujpe57.4.422.

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Exterior algebras and differential forms are widely used in many fields of modern mathematics and theoretical physics. In this work, we define a notion of N-metric exterior algebra, which depends on N matrices of structure constants. The usual exterior algebra (Grassmann algebra) can be considered as a 0-metric exterior algebra. The Clifford algebra can be considered as a 1-metric exterior algebra. N-metric exterior algebras for N ≥ 2 can be considered as generalizations of the Grassmann and Clifford algebras. Specialists consider models of gravity that are based on a mathematical formalism with two metric tensors. We hope that the 2-metric exterior algebra considered in this work can be useful for the development of this model in gravitation theory and,especially, in the description of fermions in the presence of a gravity field.
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2

Karaçuha, Serkan, and Christian Lomp. "Integral calculus on quantum exterior algebras." International Journal of Geometric Methods in Modern Physics 11, no. 04 (April 2014): 1450026. http://dx.doi.org/10.1142/s0219887814500261.

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Hom-connections and associated integral forms have been introduced and studied by Brzeziński as an adjoint version of the usual notion of a connection in non-commutative geometry. Given a flat hom-connection on a differential calculus (Ω, d) over an algebra A yields the integral complex which for various algebras has been shown to be isomorphic to the non-commutative de Rham complex (in the sense of Brzeziński et al. [Non-commutative integral forms and twisted multi-derivations, J. Noncommut. Geom.4 (2010) 281–312]). In this paper we shed further light on the question when the integral and the de Rham complex are isomorphic for an algebra A with a flat Hom-connection. We specialize our study to the case where an n-dimensional differential calculus can be constructed on a quantum exterior algebra over an A-bimodule. Criteria are given for free bimodules with diagonal or upper-triangular bimodule structure. Our results are illustrated for a differential calculus on a multivariate quantum polynomial algebra and for a differential calculus on Manin's quantum n-space.
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3

Xu, YunGe, Chao Zhang, XiaoJing Ma, and QingFeng Hu. "Hochschild cohomology of Beilinson algebra of exterior algebra." Science China Mathematics 55, no. 6 (May 30, 2012): 1153–70. http://dx.doi.org/10.1007/s11425-012-4388-9.

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4

Hawrylycz, M. "Dimension independence in exterior algebra." Proceedings of the National Academy of Sciences 92, no. 6 (March 14, 1995): 2323–27. http://dx.doi.org/10.1073/pnas.92.6.2323.

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5

Johari, Farangis, and Peyman Niroomand. "Certain functors of nilpotent Lie algebras with the derived subalgebra of dimension two." Journal of Algebra and Its Applications 19, no. 01 (March 8, 2019): 2050012. http://dx.doi.org/10.1142/s0219498820500127.

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By considering the nilpotent Lie algebra with the derived subalgebra of dimension [Formula: see text], we compute some functors including the Schur multiplier, the exterior square and the tensor square of these Lie algebras. We also give the corank of such Lie algebras.
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6

Ali, Md Showkat, K. M. Ahmed, M. R. Khan, and Md Mirazul Islam. "Exterior Algebra with Differential Forms on Manifolds." Dhaka University Journal of Science 60, no. 2 (August 3, 2012): 247–52. http://dx.doi.org/10.3329/dujs.v60i2.11528.

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The concept of an exterior algebra was originally introduced by H. Grassman for the purpose of studying linear spaces. Subsequently Elie Cartan developed the theory of exterior differentiation and successfully applied it to the study of differential geometry [8], [9] or differential equations. More recently, exterior algebra has become powerful and irreplaceable tools in the study of differential manifolds with differential forms and we develop theorems on exterior algebra with examples.DOI: http://dx.doi.org/10.3329/dujs.v60i2.11528 Dhaka Univ. J. Sci. 60(2): 247-252, 2012 (July)
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7

Kehagias, A. A. "Cuntz deformations of the exterior algebra." Journal of Physics A: Mathematical and General 26, no. 19 (October 7, 1993): L1037—L1046. http://dx.doi.org/10.1088/0305-4470/26/19/011.

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8

PIKHURKO, OLEG. "Weakly Saturated Hypergraphs and Exterior Algebra." Combinatorics, Probability and Computing 10, no. 5 (September 2001): 435–51. http://dx.doi.org/10.1017/s0963548301004746.

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Given an r-graph F, an r-graph G is called weakly F-saturated if the edges missing from G can be added, one at a time, in some order, each extra edge creating a new copy of F. Let w-sat(n, F) be the minimal size of a weakly F-saturated graph of order n. We compute the w-sat function for a wide class of r-graphs called pyramids: these include many examples for which the w-sat function was known, as well as many new examples, such as the computation of w-sat(n,Ks + Kt), and enable us to prove a conjecture of Tuza.Our main technique, developed from ideas of Kalai, is based on matroids derived from exterior algebra. We prove that if it succeeds for some graphs then the same is true for the ‘cones’ and ‘joins’ of such graphs, so that the w-sat function can be computed for many graphs that are built up from certain elementary graphs by these operations.
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9

Filliman, P. "Exterior algebra and projections of polytopes." Discrete & Computational Geometry 5, no. 3 (June 1990): 305–22. http://dx.doi.org/10.1007/bf02187792.

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10

Ramasinghe, W. "Exterior algebra of a Banach space." Bulletin des Sciences Mathématiques 131, no. 3 (April 2007): 291–324. http://dx.doi.org/10.1016/j.bulsci.2006.05.007.

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11

So, A. T. P., and W. L. Chan. "Exterior lighting design by computer algebra." Lighting Research and Technology 28, no. 2 (June 1, 1996): 89–95. http://dx.doi.org/10.1177/14771535960280020301.

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12

Bazlov, Yuri. "Graded Multiplicities in the Exterior Algebra." Advances in Mathematics 158, no. 2 (March 2001): 129–53. http://dx.doi.org/10.1006/aima.2000.1969.

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13

HE, JUNHUA, and YOUJUN TAN. "DECOMPOSABLY-GENERATED MODULES OF SIMPLE LIE ALGEBRAS." Journal of Algebra and Its Applications 11, no. 02 (April 2012): 1250023. http://dx.doi.org/10.1142/s0219498811005415.

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It is shown that there are finitely many irreducible finite-dimensional orthogonal modules V (up to isomorphism) over any complex simple Lie algebras such that Spin0(V) is decomposably-generated in the sense of Panyushev [The exterior algebra and "Spin" of an orthogonal 𝔤-module, Trans. Groups6 (2001) 371–396]. The case of simple Lie algebras of type A is discussed.
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14

Gatsé, S. C., and C. C. Likouka. "A POISSON ALGEBRA STRUCTURE OVER THE EXTERIOR ALGEBRA OF A QUADRATIC SPACE." Advances in Mathematics: Scientific Journal 12, no. 1 (January 21, 2023): 175–86. http://dx.doi.org/10.37418/amsj.12.1.11.

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15

Kämpf, Gesa, and Martina Kubitzke. "Exterior Depth and Exterior Generic Annihilator Numbers." Communications in Algebra 40, no. 1 (January 2012): 1–25. http://dx.doi.org/10.1080/00927870903386486.

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16

Fløystad, Gunnar. "Exterior algebra resolutions arising from homogeneous bundles." MATHEMATICA SCANDINAVICA 94, no. 2 (June 1, 2004): 191. http://dx.doi.org/10.7146/math.scand.a-14438.

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We describe resolutions of general maps (resp. general symmetric and skew-symmetric maps) $E^a \rightarrow E(1)^b$ given by linear forms over the exterior algebra $E$. Via the BGG-correspondence we describe the associated coherent sheaves. We also show how representation theory of algebraic groups enables one to solve these types of problems for much larger classes of maps.
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17

Nilsson, Andreas, and Jan Snellman. "Lifting Gröbner Bases from the Exterior Algebra." Communications in Algebra 31, no. 12 (January 12, 2003): 5715–25. http://dx.doi.org/10.1081/agb-120024850.

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18

Greub, W. H., and J. R. Vanstone. "A basic identity in mixed exterior algebra." Linear and Multilinear Algebra 21, no. 1 (May 1987): 41–61. http://dx.doi.org/10.1080/03081088708817778.

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19

Morgan, Frank. "The exterior algebra ΛkRn and area minimization." Linear Algebra and its Applications 66 (April 1985): 1–28. http://dx.doi.org/10.1016/0024-3795(85)90123-5.

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20

Kupriyanov, Vladislav G., and Richard J. Szabo. "Symplectic embeddings, homotopy algebras and almost Poisson gauge symmetry." Journal of Physics A: Mathematical and Theoretical 55, no. 3 (December 28, 2021): 035201. http://dx.doi.org/10.1088/1751-8121/ac411c.

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Abstract We formulate general definitions of semi-classical gauge transformations for noncommutative gauge theories in general backgrounds of string theory, and give novel explicit constructions using techniques based on symplectic embeddings of almost Poisson structures. In the absence of fluxes the gauge symmetries close a Poisson gauge algebra and their action is governed by a P ∞-algebra which we construct explicitly from the symplectic embedding. In curved backgrounds they close a field dependent gauge algebra governed by an L ∞-algebra which is not a P ∞-algebra. Our technique produces new all orders constructions which are significantly simpler compared to previous approaches, and we illustrate its applicability in several examples of interest in noncommutative field theory and gravity. We further show that our symplectic embeddings naturally define a P ∞-structure on the exterior algebra of differential forms on a generic almost Poisson manifold, which generalizes earlier constructions of differential graded Poisson algebras, and suggests a new approach to defining noncommutative gauge theories beyond the gauge sector and the semi-classical limit based on A ∞-algebras.
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21

Reeder, Mark. "Exterior Powers of the Adjoint Representation." Canadian Journal of Mathematics 49, no. 1 (February 1, 1997): 133–59. http://dx.doi.org/10.4153/cjm-1997-007-1.

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22

Eisenbud, David. "Periodic resolutions over exterior algebras." Journal of Algebra 258, no. 1 (December 2002): 348–61. http://dx.doi.org/10.1016/s0021-8693(02)00511-2.

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23

Thieu, Phong Dinh. "Universally Koszul and initially Koszul properties of Orlik–Solomon algebras." Journal of Algebra and Its Applications 19, no. 11 (November 18, 2019): 2050218. http://dx.doi.org/10.1142/s0219498820502187.

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Let [Formula: see text] be a field with [Formula: see text] and [Formula: see text] an exterior algebra over [Formula: see text] with a standard grading [Formula: see text]. Let [Formula: see text] be a graded algebra, where [Formula: see text] is a graded ideal in [Formula: see text]. In this paper, we study universally Koszul and initially Koszul properties of [Formula: see text] and find classes of ideals [Formula: see text] which characterize such properties of [Formula: see text]. As applications, we classify arrangements whose Orlik–Solomon algebras are universally Koszul or initially Koszul. These results are related to a long-standing question of Shelton–Yuzvinsky [B. Shelton and S. Yuzvinsky, Koszul algebras from graphs and hyperplane arrangements, J. London Math. Soc. 56 (1997) 477–490].
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24

Tam, Hon-wah, and Yu-feng Zhang. "An approach for constructing loop algebra via exterior algebra and its applications." Chaos, Solitons & Fractals 23, no. 2 (January 2005): 535–41. http://dx.doi.org/10.1016/j.chaos.2004.05.007.

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25

De Concini, Corrado, Paolo Papi, and Claudio Procesi. "The adjoint representation inside the exterior algebra of a simple Lie algebra." Advances in Mathematics 280 (August 2015): 21–46. http://dx.doi.org/10.1016/j.aim.2015.04.011.

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26

De Concini, Corrado, Pierluigi Möseneder Frajria, Paolo Papi, and Claudio Procesi. "On special covariants in the exterior algebra of a simple Lie algebra." Rendiconti Lincei - Matematica e Applicazioni 25, no. 3 (2014): 331–44. http://dx.doi.org/10.4171/rlm/682.

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27

FIALOWSKI, ALICE, and MICHAEL PENKAVA. "VERSAL DEFORMATIONS OF THREE-DIMENSIONAL LIE ALGEBRAS AS L∞ ALGEBRAS." Communications in Contemporary Mathematics 07, no. 02 (April 2005): 145–65. http://dx.doi.org/10.1142/s0219199705001702.

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We consider versal deformations of 0|3-dimensional L∞ algebras, also called strongly homotopy Lie algebras, which correspond precisely to ordinary (non-graded) three-dimensional Lie algebras. The classification of such algebras is well-known, although we shall give a derivation of this classification using an approach of treating them as L∞ algebras. Because the symmetric algebra of a three-dimensional odd vector space contains terms only of exterior degree less than or equal to three, the construction of versal deformations can be carried out completely. We give a characterization of the moduli space of Lie algebras using deformation theory as a guide to understanding the picture.
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28

Eisenbud, David, Irena Peeva, and Frank-Olaf Schreyer. "Tor as a module over an exterior algebra." Journal of the European Mathematical Society 21, no. 3 (November 29, 2018): 873–96. http://dx.doi.org/10.4171/jems/853.

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29

Fløystad, Gunnar. "The Exterior Algebra and Central Notions in Mathematics." Notices of the American Mathematical Society 62, no. 04 (April 1, 2015): 364–71. http://dx.doi.org/10.1090/noti1234.

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30

Walter, Charles, Frank-Olaf Schreyer, Sorin Popescu, and David Eisenbud. "Exterior algebra methods for the minimal resolution conjecture." Duke Mathematical Journal 112, no. 2 (April 2002): 379–95. http://dx.doi.org/10.1215/s0012-9074-02-11226-5.

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31

Koç, Cemal, and Songül Esin. "ANNIHILATORS OF PRINCIPAL IDEALS IN THE EXTERIOR ALGEBRA." Taiwanese Journal of Mathematics 11, no. 4 (September 2007): 1019–35. http://dx.doi.org/10.11650/twjm/1500404799.

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32

Lundqvist, Samuel, and Lisa Nicklasson. "On generic principal ideals in the exterior algebra." Journal of Pure and Applied Algebra 223, no. 6 (June 2019): 2615–34. http://dx.doi.org/10.1016/j.jpaa.2018.09.011.

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33

Molinuevo, Ariel. "Deformations of the exterior algebra of differential forms." Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry 57, no. 4 (May 30, 2016): 771–87. http://dx.doi.org/10.1007/s13366-016-0299-1.

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34

El Baz, M., and Y. Hassouni. "Deformed Exterior Algebra, Quons and their Coherent States." International Journal of Modern Physics A 18, no. 17 (July 10, 2003): 3015–40. http://dx.doi.org/10.1142/s0217751x03015386.

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We review the notion of the deformation of the exterior wedge product. This allows us to construct the deformation of the algebra of exterior forms over a vector space and also over an arbitrary manifold. We relate this approach to the generalized statistics. We study quons, as a particular case of these generalized statistics. We also give their statistical properties. A large part of the work is devoted to the problem of constructing coherent states for the deformed oscillators. We give a review of all the approaches existing in the literature concerning this point and enforce it with many examples.
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35

Nagel, Uwe, Tim Römer, and Natale Paolo Vinai. "Algebraic Shifting and Exterior and Symmetric Algebra Methods." Communications in Algebra 36, no. 1 (January 16, 2008): 208–31. http://dx.doi.org/10.1080/00927870701665321.

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36

Allen, Leanne, and Thomas J. Bridges. "Numerical exterior algebra and the compound matrix method." Numerische Mathematik 92, no. 2 (August 1, 2002): 197–232. http://dx.doi.org/10.1007/s002110100365.

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37

NERSESSIAN, A. "ANTIBRACKETS AND NON-ABELIAN EQUIVARIANT COHOMOLOGY." Modern Physics Letters A 10, no. 39 (December 21, 1995): 3043–49. http://dx.doi.org/10.1142/s0217732395003173.

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38

Allday, C., and V. Puppe. "On a Conjecture of Goresky, Kottwitz and MacPherson." Canadian Journal of Mathematics 51, no. 1 (February 1, 1999): 3–9. http://dx.doi.org/10.4153/cjm-1999-001-4.

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AbstractWe settle a conjecture of Goresky, Kottwitz and MacPherson related to Koszul duality, i.e., to the correspondence between differential graded modules over the exterior algebra and those over the symmetric algebra.
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39

TSUTSUMI, YUKIHIRO. "KNOTTED SEIFERT SURFACES AND UNKNOTTED SEIFERT SURFACES." Journal of Knot Theory and Its Ramifications 17, no. 02 (February 2008): 141–55. http://dx.doi.org/10.1142/s0218216508006038.

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It is known that free genus one knots do not admit Seifert surfaces with hyperbolic exteriors. In this paper, for any integer g ≥ 2, we exhibit a knot of genus g which bounds a minimal genus Seifert surface with hyperbolic exterior and a minimal genus free Seifert surface.
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40

Ahmed, Khondokar M., and Saraban Tahora. "Multilinear Algebras and Tensors with Vector Subbundle of Manifolds." Dhaka University Journal of Science 62, no. 1 (February 7, 2015): 31–35. http://dx.doi.org/10.3329/dujs.v62i1.21957.

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In the present paper some aspects of tensor algebra, tensor product, exterior algebra, symmetric algebra, module of section, graded algebra, vector subbundle are studied. A Theorem 1.32. is established by using sections and fibrewise orthogonal sections of an application of Gran-Schmidt. DOI: http://dx.doi.org/10.3329/dujs.v62i1.21957 Dhaka Univ. J. Sci. 62(1): 31-35, 2014 (January)
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41

Shakin, D. A. "Piecewise lexsegment ideals in exterior algebras." Sbornik: Mathematics 196, no. 2 (February 28, 2005): 287–307. http://dx.doi.org/10.1070/sm2005v196n02abeh000881.

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42

González D'León, Rafael S. "The colored symmetric and exterior algebras." Journal of Algebra 496 (February 2018): 187–215. http://dx.doi.org/10.1016/j.jalgebra.2017.10.013.

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43

Xu, Yunge, and Yang Han. "Hochschild (Co)homology of Exterior Algebras." Communications in Algebra 35, no. 1 (December 26, 2006): 115–31. http://dx.doi.org/10.1080/00927870601041375.

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44

Sköldberg, Emil. "Monomial Golod Quotients of Exterior Algebras." Journal of Algebra 218, no. 1 (August 1999): 183–89. http://dx.doi.org/10.1006/jabr.1998.7826.

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45

Guo, Jinyun, Qiuxian Wu, and Qianhong Wan. "On the Tubes of Exterior Algebras." Algebra Colloquium 13, no. 01 (March 2006): 149–62. http://dx.doi.org/10.1142/s1005386706000162.

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In this paper, we study the Koszul modules of complexity 1 of an exterior algebra of a vector space V over an algebraically closed field. We prove that there are ℙ (V)-orthogonal families of such modules, each of which consists of Koszul modules filtered by the cyclic ones corresponding to the same point in ℙ (V). We also prove that they are invariant under syzygy, so they are all on the homogeneous tubes.
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46

KIRILLOV, ANATOL N. "DECOMPOSITION OF SYMMETRIC AND EXTERIOR POWERS OF THE ADJOINT REPRESENTATION OF ${\mathfrak g}l_N$ 1: UNIMODALITY OF PRINCIPAL SPECIALIZATION OF THE INTERNAL PRODUCT OF THE SCHUR FUNCTIONS." International Journal of Modern Physics A 07, supp01b (April 1992): 545–79. http://dx.doi.org/10.1142/s0217751x92003938.

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The problem of decomposing the symmetric and exterior algebras of the adjoint representation of the Lie algebra [Formula: see text] into [Formula: see text]-irreducible components are considered. The exact formula for the principal specialization of the internal product of the Schur functions (similar to the formula for Kostka-Foulkes polynomials) is obtained by the purely combinatorial approach, based on the theory of rigged configurations. The stable behaviour of some polynomials is studied. Different examples are presented.
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47

SATO, YOSHIHISA. "THE REFLEXIVITY OF 2-KNOTS IN S2 × S2." Journal of Knot Theory and Its Ramifications 01, no. 01 (March 1992): 21–29. http://dx.doi.org/10.1142/s0218216592000033.

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We consider a locally flat 2-sphere embedded in S2 × S2, which is referred to as a 2-knot in S2 × S2, and we study the problem whether a 2-knot in S2 × S2 is determined by its exterior. In this paper, we show that for almost homology classes ξ, 2-knots in S2 × S2 representing ξ are determined by their exteriors.
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48

Eisenbud, David, Sorin Popescu, and Sergey Yuzvinsky. "Hyperplane arrangement cohomology and monomials in the exterior algebra." Transactions of the American Mathematical Society 355, no. 11 (July 10, 2003): 4365–83. http://dx.doi.org/10.1090/s0002-9947-03-03292-6.

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49

Yanagawa, Kohji. "BGG Correspondence and Römer’s Theorem on an Exterior Algebra." Algebras and Representation Theory 9, no. 6 (September 14, 2006): 569–79. http://dx.doi.org/10.1007/s10468-006-9037-y.

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50

Peeva, Irena, and Mike Stillman. "Flips and the Hilbert scheme over an exterior algebra." Mathematische Annalen 339, no. 3 (June 6, 2007): 545–57. http://dx.doi.org/10.1007/s00208-007-0122-2.

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