Relevant bibliographies by topics / Abelian structures

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

Academic literature on the topic 'Abelian structures'

Author: Grafiati
Published: 28 September 2024

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Journal articles on the topic "Abelian structures"

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Lu, Jianwei, and Liguo He. "On the Structures of Abelianπ-Regular Rings." International Journal of Mathematics and Mathematical Sciences 2014 (2014): 1–4. http://dx.doi.org/10.1155/2014/842313.

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Assume thatRis an Abelian ring. In this paper, we characterize the structure ofRwheneverRisπ-regular. It is also proved that an Abelianπ-regular ring is isomorphic to the subdirect sum of some metadivision rings.
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Clarke, Francis. "Counting abelian group structures." Proceedings of the American Mathematical Society 134, no. 10 (April 10, 2006): 2795–99. http://dx.doi.org/10.1090/s0002-9939-06-08396-1.

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CONSOLE, S., A. FINO, and Y. S. POON. "STABILITY OF ABELIAN COMPLEX STRUCTURES." International Journal of Mathematics 17, no. 04 (April 2006): 401–16. http://dx.doi.org/10.1142/s0129167x06003576.

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Let M = Γ\G be a nilmanifold endowed with an invariant complex structure. We prove that Kuranishi deformations of abelian complex structures are all invariant complex structures, generalizing a result in [7] for 2-step nilmanifolds. We characterize small deformations that remain abelian. As an application, we observe that at real dimension six, the deformation process of abelian complex structures is stable within the class of nilpotent complex structures. We give an example to show that this property does not hold in higher dimension.
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Poon, Yat Sun. "Abelian Complex Structures and Generalizations." Complex Manifolds 8, no. 1 (January 1, 2021): 247–66. http://dx.doi.org/10.1515/coma-2020-0117.

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Abstract After a review on the development of deformation theory of abelian complex structures from both the classical and generalized sense, we propose the concept of semi-abelian generalized complex structure. We present some observations on such structure and illustrate this new concept with a variety of examples.
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Tang, Guoliang. "Abelian model structures on comma categories." Ukrains’kyi Matematychnyi Zhurnal 76, no. 3 (March 25, 2024): 373–81. http://dx.doi.org/10.3842/umzh.v76i3.7289.

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UDC 512.64 Let A and B be bicomplete Abelian categories, which both have enough projectives and injectives and let T : A → B be a right exact functor. Under some mild conditions, we show that hereditary Abelian model structures on A and B can be amalgamated into a global hereditary Abelian model structure on the comma category ( T ↓ B ) . As an application of this result, we give an explicit description of a subcategory that consists of all trivial objects of the Gorenstein flat model structure on the category of modules over a triangular matrix ring.
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Goswami, Amartya. "Salamander lemma for non-abelian group-like structures." Journal of Algebra and Its Applications 19, no. 02 (March 15, 2019): 2050022. http://dx.doi.org/10.1142/s021949882050022x.

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It is well known that the classical diagram lemmas of homological algebra for abelian groups can be generalized to non-abelian group-like structures, such as groups, rings, algebras, loops, etc. In this paper, we establish such a generalization of the “salamander lemma” due to G. M. Bergman, in a self-dual axiomatic context (developed originally by Z. Janelidze), which applies to all usual non-abelian group-like structures and also covers axiomatic contexts such as semi-abelian categories in the sense of G. Janelidze, L. Márki and W. Tholen and exact categories in the sense of M. Grandis.
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Yu, Chia-Fu. "Abelian varieties over finite fields as basic abelian varieties." Forum Mathematicum 29, no. 2 (March 1, 2017): 489–500. http://dx.doi.org/10.1515/forum-2014-0141.

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AbstractIn this note we show that any basic abelian variety with additional structures over an arbitrary algebraically closed field of characteristic ${p>0}$ is isogenous to another one defined over a finite field. We also show that the category of abelian varieties over finite fields up to isogeny can be embedded into the category of basic abelian varieties with suitable endomorphism structures. Using this connection, we derive a new mass formula for a finite orbit of polarized abelian surfaces over a finite field.
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Fokina, E., J. F. Knight, A. Melnikov, S. M. Quinn, and C. Safranski. "Classes of Ulm type and coding rank-homogeneous trees in other structures." Journal of Symbolic Logic 76, no. 3 (September 2011): 846–69. http://dx.doi.org/10.2178/jsl/1309952523.

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AbstractThe first main result isolates some conditions which fail for the class of graphs and hold for the class of Abelianp-groups, the class of Abelian torsion groups, and the special class of “rank-homogeneous” trees. We consider these conditions as a possible definition of what it means for a class of structures to have “Ulm type”. The result says that there can be no Turing computable embedding of a class not of Ulm type into one of Ulm type. We apply this result to show that there is no Turing computable embedding of the class of graphs into the class of “rank-homogeneous” trees. The second main result says that there is a Turing computable embedding of the class of rank-homogeneous trees into the class of torsion-free Abelian groups. The third main result says that there is a “rank-preserving” Turing computable embedding of the class of rank-homogeneous trees into the class of Boolean algebras. Using this result, we show that there is a computable Boolean algebra of Scott rank.
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Remm, Elisabeth, and Michel Goze. "Affine structures on abelian Lie groups." Linear Algebra and its Applications 360 (February 2003): 215–30. http://dx.doi.org/10.1016/s0024-3795(02)00452-4.

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Yu, Chia-Fu. "Lifting abelian varieties with additional structures." Mathematische Zeitschrift 242, no. 3 (April 1, 2002): 427–41. http://dx.doi.org/10.1007/s002090100350.

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Dissertations / Theses on the topic "Abelian structures"

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Steine, Asgeir Bertelsen. "STABILITY STRUCTURES FOR ABELIAN AND TRIANGULATED CATEGORIES." Thesis, Norwegian University of Science and Technology, Department of Mathematical Sciences, 2007. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-9603.

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This thesis is intended to present some developments in the theory of algebraic stability. The main topics are stability for triangulated categories and the distinguished slopes of Hille and de la Pena for quiver representations.

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Zatloukal, Kevin C. (Kevin Chaffee). "Applications of abelian algebraic structures in quantum computation." Thesis, Massachusetts Institute of Technology, 2016. http://hdl.handle.net/1721.1/106102.

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Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.
Cataloged from PDF version of thesis.
Includes bibliographical references (pages 163-168).
Shor's groundbreaking algorithms for integer factoring and discrete logarithm [58], along with their later generalizations 116, 35, 49, 18], demonstrated a unique ability of quantum computers to solve problems defined on abelian groups. In this thesis, we study ways in which that ability can be leveraged in order to solve problems on more complex structures such as non-abelian groups and hypergroups. This leads to new quantum algorithms for the hidden subgroup problem on nilpotent groups whose order is a product of large primes, the hidden subhypergroup problem on both strongly integral hypergroups and ultragroups, testing equivalence of group extensions, and computing the component parts of the cohomology groups of both group extensions and a generalization of simplicial complexes, amongst other problems. For each of those listed, we also show that no classical algorithm can achieve similar efficiency under standard cryptographic assumptions.
by Kevin C. Zatloukal.
Ph. D.
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Barker, Russell. "L#kappa#-equivalence and Hanf functions for finite structures." Thesis, University of Oxford, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.270249.

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Tsui, Ho-yu. "Families of polarized abelian varieties and a construction of Kähler metrics of negative holomorphic bisectional curvature on Kodaira surfaces." Click to view the E-thesis via HKUTO, 2006. http://sunzi.lib.hku.hk/hkuto/record/B37053760.

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Tsui, Ho-yu, and 徐浩宇. "Families of polarized abelian varieties and a construction of Kähler metrics of negative holomorphic bisectional curvature on Kodairasurfaces." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2006. http://hub.hku.hk/bib/B37053760.

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Hossain, Akash. "Forking in valued fields and related structures." Electronic Thesis or Diss., université Paris-Saclay, 2024. http://www.theses.fr/2024UPASM019.

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Cette thèse est une contribution à la théorie des modèles des corps valués. On étudie la déviation dans les corps valués, ainsi que certains de leurs réduits. On s'intéresse particulièrement aux corps pseudo-locaux, les ultraproduits de caractéristique résiduelle nulle des corps valués p-adiques. Nous considérons d'abord aux groupes des valeurs des corps valués qui nous intéressent, les groupes Abéliens ordonnés réguliers. Nous y établissons description géométrique de la déviation, ainsi qu'une classification détaillée des extensions globales non-déviantes ou invariantes d'un type donné. Nous démontrons ensuite des principes d'Ax-Kochen-Ershov pour la division et la déviation dans la théorie resplendissante des expansions de suites exactes courtes pures de structures Abéliennes, telles qu'étudiées dans l'article sur la distalité d'Aschenbrenner-Chernikov-Gehret-Ziegler. En particulier, nos résultats s'appliquent aux groupes des termes dominants des (expansions de) corps valués. Pour finir, nous donnons diverses conditions suffisantes pour qu'un ensemble de paramètres soit une base d'extension dans un corps valué Hensélien de caractéristique résiduelle nulle. En particulier, nous démontrons que la déviation coïncide avec la division dans les corps pseudo-locaux de caractéristique résiduelle nulle. Nous discutons aussi des résultats de Ealy-Haskell-Simon sur la déviation pour les extensions séparées de corps valués Henséliens de caractéristique résiduelle nulle. Nous contribuons à la question en démontrant que, dans le cas d'une extension Abhyankar, et avec quelques hypothèses supplémentaires, la non-déviation d'un type dans in corps pseudo-local implique l'existence d'une mesure de Keisler globale invariante dont le support contient ce type, à l'instar des corps pseudo-finis
This thesis is a contribution to the model theory of valued fields. We study forking in valued fields and some of their reducts. We focus particularly on pseudo-local fields, the ultraproducts of residue characteristic zero of the p-adic valued fields. First, we look at the value groups of the valued fields we are interested in, the regular ordered Abelian groups. We establish for these ordered groups a geometric description of forking, as well as a full classification of the global extensions of a given type which are non-forking or invariant. Then, we prove an Ax-Kochen-Ershov principle for forking and dividing in expansions of pure short exact sequences of Abelian structures, as studied by Aschenbrenner-Chernikov-Gehret-Ziegler in their article about distality. This setting applies in particular to the leading-term structure of (expansions of) valued fields. Lastly, we give various sufficient conditions for a parameter set in a Henselian valued field of residue characteristic zero to be an extension base. In particular, we show that forking equals dividing in pseudo-local of residue characteristic zero. Additionally, we discuss results by Ealy-Haskell-Simon on forking in separated extensions of Henselian valued fields of residue characteristic zero. We contribute to the question in the setting of Abhyankar extensions, where we show that, with some additional conditions, if a type in a pseudo-local field does not fork, then there exists some global invariant Keisler measure whose support contains that type. This behavior is well-known in pseudo-finite fields
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Kuroda, Kunihiko. "Abelian conformal field theory with level structure." 京都大学 (Kyoto University), 2007. http://hdl.handle.net/2433/136737.

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Milliet, Cédric. "Propriétés algébriques des structures menues ou minces, rang de Cantor Bendixson, espaces topologiques généralisés." Phd thesis, Université Claude Bernard - Lyon I, 2009. http://tel.archives-ouvertes.fr/tel-00442772.

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Les structures menues apparaissent dans les années 1960 de paire avec la conjecture de Vaught, dont elles sont les seuls contre-exemples possibles. Les structures minces sont introduites par Belegradek, et englobent à la fois les structures minimales et menues. Il est bien connu que les ensembles définissables d'une structure mince sont rangés par le rang de Cantor-Bendixson, lorsque l'on fixe un ensemble fini de paramètres. L'étude de ces structures est rendue difficile par le fait que si l'on augmente cet ensemble de paramètres, le rang croît, et on ne sait maîtriser sa croissance. Nous présentons des propriétés de calcul de ce rang, une condition de chaîne descendante locale sur les groupes définissables (par des formules faisant intervenir des paramètres de la clôture algébrique d'un ensemble fini), ainsi qu'une notion de presque stabilisateur local. Nous en déduisons des propriétés algébriques des structures minces : un corps mince de caractéristique positive est localement de dimension finie sur son centre (une réponse au problème 6.1.5 de Wagner, Simple Theories), et un groupe mince infini a un sous groupe abélien infini (cela répond en particulier à la question 2.8 de Wagner, "Groups in simple theories"). Nous nous intéressons ensuite aux structures menues infiniment définissables, et montrons que les groupes d'arité finie infiniment définissables (par des formules n'utilisant que les paramètres d'un ensemble fini) sont l'intersection de groupes définissables (réponse au problème 6.1.14 du livre de Wagner). Nous étendons le résultat aux demi-groupes, anneaux, corps, catégories et groupoïdes infiniment définissables (toujours avec un nombre fini de paramètres), et donnons des résultats de définissabilité locale pour les groupes et corps simples et menus, infiniment définissables sur un ensemble quelconque de paramètres. Enfin, nous réintroduisons le rang de Cantor dans son contexte topologique et montrons que la dérivée de Cantor peut être vue comme un opérateur de dérivation dans un semi-anneau d'espaces topologiques. Dans l'idée de trouver un rang de Cantor global pour les théories stables, nous essayons de nous débarrasser du mot dénombrable omniprésent lorsque l'on fait de la topologie, en le remplaçant par un cardinal régulier k. Nous développons une notion d'espace k-métrique, de k-topologie, de k-compacité etc. et montrons un k-analogue du lemme de métrisabilité d'Urysohn, et du théorème de Cantor-Bendixson.
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King, Malcolm Bruce. "A structure theorem for asymptotically abelian W*-dynamical systems." Diss., University of Pretoria, 2016. http://hdl.handle.net/2263/60817.

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We prove a partial non-commutative analogue of the Furstenberg-Zimmerman Structure Theorem, originally proved by Tim Austin, Tanya Eisner and Terence Tao. In Chapter 1, we review the GNS construction for states on von Neumann algebras and the related semicyclic representation for tracial weights. We look at Tomita- Takasaki theory in the special case of traces. This will allow us to introduce the Jones projection and conditional expectations of von Neumann algebras. We then de ne the basic construction and its associated nite lifted trace. We also introduce the notion of projections of nite lifted trace and how they relate to right submodules. Chapter 2 introduces dynamics in the form of automorphisms on von Neumamnn algebras. We will see how the dynamics is represented on the GNS Hilbert space using a cyclic and separating vector. It is then shown how the dynamics is extended to the basic construction and the semicyclic representation. The last three chapters form the \core". At the beginning of each aforementioned chapter, we present a summary of the required theory, before providing detailed proofs. In Chapter 3, we prove one of two \fundamental lemmas" where we introduce some non-commutative integration theory. We use a version of the spectral theorem expressed in terms of a spectral measure to produce a certain projection of nite lifted trace. In Chapter 4, we prove our next fundamental lemma. We use direct integral theory in order to obtain a representation of the dynamics, in terms of a module basis, on the image of the projection of nite lifted trace. In Chapter 5, we apply our previous results to asymptotically abelian W*-dynamical systems, culminating in the proof of the titular theorem.
Dissertation (MSc)--University of Pretoria, 2016.
Mathematics and Applied Mathematics
MSc
Unrestricted
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Mo, Sjur. "Phase structure and critical properties of an abelian gauge theory." Doctoral thesis, Norwegian University of Science and Technology, Department of Physics, 2002. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-443.

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Chapter 1 to 4 give a short introduction to superconductivity, microscopic theory, phase transitions, and Monte-Carlo simulations. Chapter 2 is about Cooper pairing in different settings, but I also give a short introduction to the Hofstadter problem of lattice fermions on a square lattice in a perpendicular magnetic field. The purpose is to clarify some points in Paper-I. Chapter 3 is about phase transitions, and introduces the important concepts of spontaneous symmetry breaking, scaling, and renormalization. In the last section I stress some of the main differences between first order and second order phase transitions. Chapter 4 starts with a short elementary introduction to Monte-Carlo simulations and proceeds with the important, but somewhat more advanced topic of reweighting.

Chapter 5 to 7 are more closely related to the specific projects I have worked on, and are meant to illuminate and clarify some aspects in Paper-II and Paper-III. Chapter 5 introduce the Ginzburg-Landau model in various parametrizations, present some perturbative (mean-field) results, and introduce the concept of topological defects (vortices) and duality.

Chapter 6 is closely related to Paper-II and introduce the concept of fractal dimension and the relation between the vortex excitations of the original theory and the dual field theory. Chapter 7 is closely related to Paper-III where we studied the order of the metal to superconductor phase transition. To do this we had to do infinite volume and continuum limit extrapolations. We also had to consider ultraviolet renormalization since the Ginzburg-Landau theory is a continuum field theory with no inherent short scale cut-off. To reduce auto-correlation times we added several improvements to the standard Metropolis algorithm in the Monte-Carlo simulations, the most important being an overrelaxation algorithm for the scalar field and a global update of the scalar amplitude.

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Books on the topic "Abelian structures"

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Borceux, Francis. Handbook of categorical algebra 2: Categories and structures. Cambridge [England]: Cambridge University Press, 1994.

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Marszałek, Roman. Galois module structure of the group of units of real Abelian fields. Opole: Wydawnictwo Uniwersytetu Opolskiego, 2011.

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Heyer, Herbert. Structural aspects in the theory of probability. 2nd ed. New Jersey: World Scientific, 2009.

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Pantev, Tony. Stacks and catetories in geometry, topology, and algebra: CATS4 Conference Higher Categorical Structures and Their Interactions with Algebraic Geometry, Algebraic Topology and Algebra, July 2-7, 2012, CIRM, Luminy, France. Providence, Rhode Island: American Mathematical Society, 2015.

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Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View toward Coherent Sheaves (2006 Cambridge, Mass.). Grassmannians, moduli spaces, and vector bundles: Clay Mathematics Institute Workshop on Moduli Spaces of Vector Bundles, with a View towards Coherent Sheaves, October 6-11, 2006, Cambridge, Massachusetts. Edited by Ellwood D. (David) 1966- and Previato Emma. Providence, RI: American Mathematical Society, 2011.

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J, Sally Paul. Fundamentals of mathematical analysis. Providence, Rhode Island: American Mathematical Society, 2013.

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Simon, Barry. Operator theory. Providence, Rhode Island: American Mathematical Society, 2015.

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Loth, Peter, and Carol Jacoby. Abelian Groups: Structures and Classifications. De Gruyter, Inc., 2019.

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Loth, Peter, and Carol Jacoby. Abelian Groups: Structures and Classifications. de Gruyter GmbH, Walter, 2019.

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Loth, Peter, and Carol Jacoby. Abelian Groups: Structures and Classifications. de Gruyter GmbH, Walter, 2019.

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Book chapters on the topic "Abelian structures"

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Adler, Allan, and Sundararaman Ramanan. "Theta structures and the addition formula." In Moduli of Abelian Varieties, 31–51. Berlin, Heidelberg: Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0093663.

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Šťovíček, Jan. "Abelian Model Structures and Applications." In Trends in Mathematics, 155–59. Cham: Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-45441-2_27.

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Dvurečenskij, Anatolij, and Sylvia Pulmannová. "Quotients of Partial Abelian Monoids." In New Trends in Quantum Structures, 191–229. Dordrecht: Springer Netherlands, 2000. http://dx.doi.org/10.1007/978-94-017-2422-7_4.

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Moonen, Ben. "Group Schemes with Additional Structures and Weyl Group Cosets." In Moduli of Abelian Varieties, 255–98. Basel: Birkhäuser Basel, 2001. http://dx.doi.org/10.1007/978-3-0348-8303-0_10.

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Marra, Vincenzo, and Daniele Mundici. "MV-Algebras and Abelian l-Groups: a Fruitful Interaction." In Ordered Algebraic Structures, 57–88. Boston, MA: Springer US, 2002. http://dx.doi.org/10.1007/978-1-4757-3627-4_4.

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Lucas, F. "Some Applications of Definable Spine Analysis in Ordered Abelian Groups." In Ordered Algebraic Structures, 123–28. Dordrecht: Springer Netherlands, 1989. http://dx.doi.org/10.1007/978-94-009-2472-7_10.

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Nikolić-Despotović, Danica, and Stevan Pilipović. "Abelian Theorem for the Distributional Stieltjes Transformation." In Generalized Functions, Convergence Structures, and Their Applications, 139–46. Boston, MA: Springer US, 1988. http://dx.doi.org/10.1007/978-1-4613-1055-6_13.

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Lurie, Jacob. "Full Level Structures on Elliptic Curves." In p-adic Hodge Theory, Singular Varieties, and Non-Abelian Aspects, 239–52. Cham: Springer International Publishing, 2022. http://dx.doi.org/10.1007/978-3-031-21550-6_5.

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Abu Zaid, F., E. Grädel, M. Grohe, and W. Pakusa. "Choiceless Polynomial Time on Structures with Small Abelian Colour Classes." In Mathematical Foundations of Computer Science 2014, 50–62. Berlin, Heidelberg: Springer Berlin Heidelberg, 2014. http://dx.doi.org/10.1007/978-3-662-44522-8_5.

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Dekimpe, Karel, and Paul Igodt. "Polynomial structures for iterated central extensions of abelian-by-nilpotent groups." In Algebraic Topology: New Trends in Localization and Periodicity, 155–66. Basel: Birkhäuser Basel, 1996. http://dx.doi.org/10.1007/978-3-0348-9018-2_10.

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Conference papers on the topic "Abelian structures"

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Akhmedov, Emil T. "Non-Abelian structures in BSFT and RR couplings." In STRING THEORY; 10th Tohwa University International Symposium on String Theory. AIP, 2002. http://dx.doi.org/10.1063/1.1454352.

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Vezzoni, Luigi, Carlos Herdeiro, and Roger Picken. "Abelian complex structures on 2-step nilmanifolds and flat connections." In XIX INTERNATIONAL FALL WORKSHOP ON GEOMETRY AND PHYSICS. AIP, 2011. http://dx.doi.org/10.1063/1.3599135.

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Itoh, Taichi, and Yoonbai Kim. "Fixed point structure of 3D abelian gauge theories." In New directions in quantum chromodynamics. AIP, 1999. http://dx.doi.org/10.1063/1.1301677.

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Krithivasan, Dinesh, and S. Sandeep Pradhan. "Distributed source coding using Abelian group codes: Extracting performance from structure." In 2008 46th Annual Allerton Conference on Communication, Control, and Computing. IEEE, 2008. http://dx.doi.org/10.1109/allerton.2008.4797745.

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APPELQUIST, THOMAS, and L. C. R. WIJEWARDHANA. "PHASE STRUCTURE OF NON-COMPACT QED3 AND THE ABELIAN HIGGS MODEL." In Proceedings of the 3rd International Symposium. WORLD SCIENTIFIC, 2004. http://dx.doi.org/10.1142/9789812702340_0022.

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