Leibniz Algebras

Author : Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov
Publisher : CRC Press
Page : 157 pages
File Size : 48,6 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000740400

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Leibniz Algebras by Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov Pdf

Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts

Author : Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov
Publisher : CRC Press
Page : 325 pages
File Size : 42,9 Mb
Release : 2019-11-11
Category : Mathematics
ISBN : 9781000740004

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Leibniz Algebras by Shavkat Ayupov,Bakhrom Omirov,Isamiddin Rakhimov Pdf

Leibniz Algebras: Structure and Classification is designed to introduce the reader to the theory of Leibniz algebras. Leibniz algebra is the generalization of Lie algebras. These algebras preserve a unique property of Lie algebras that the right multiplication operators are derivations. They first appeared in papers of A.M Blokh in the 1960s, under the name D-algebras, emphasizing their close relationship with derivations. The theory of D-algebras did not get as thorough an examination as it deserved immediately after its introduction. Later, the same algebras were introduced in 1993 by Jean-Louis Loday , who called them Leibniz algebras due to the identity they satisfy. The main motivation for the introduction of Leibniz algebras was to study the periodicity phenomena in algebraic K-theory. Nowadays, the theory of Leibniz algebras is one of the more actively developing areas of modern algebra. Along with (co)homological, structural and classification results on Leibniz algebras, some papers with various applications of the Leibniz algebras also appear now. However, the focus of this book is mainly on the classification problems of Leibniz algebras. Particularly, the authors propose a method of classification of a subclass of Leibniz algebras based on algebraic invariants. The method is applicable in the Lie algebras case as well. Features: Provides a systematic exposition of the theory of Leibniz algebras and recent results on Leibniz algebras Suitable for final year bachelor's students, master's students and PhD students going into research in the structural theory of finite-dimensional algebras, particularly, Lie and Leibniz algebras Covers important and more general parts of the structural theory of Leibniz algebras that are not addressed in other texts

Author : Viktor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov
Publisher : Springer Science & Business Media
Page : 431 pages
File Size : 50,7 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9783642572012

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Computer Algebra in Scientific Computing by Viktor G. Ganzha,Ernst W. Mayr,Evgenii V. Vorozhtsov Pdf

Proceedings of the Third Workshop on Computer Algebra in Scientific Computing, Samarkand, Octobe5r 5-9, 2000

Author : Helena Albuquerque,Jose Brox,Consuelo Martínez,Paulo Saraiva
Publisher : Springer Nature
Page : 305 pages
File Size : 48,6 Mb
Release : 2023-07-28
Category : Mathematics
ISBN : 9783031327070

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Non-Associative Algebras and Related Topics by Helena Albuquerque,Jose Brox,Consuelo Martínez,Paulo Saraiva Pdf

This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.

Author : Naihuan Jing,Kailash C. Misra
Publisher : American Mathematical Soc.
Page : 233 pages
File Size : 49,6 Mb
Release : 2018-08-21
Category : Algebra
ISBN : 9781470436964

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Representations of Lie Algebras, Quantum Groups and Related Topics by Naihuan Jing,Kailash C. Misra Pdf

This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.

Author : Sergei Silvestrov,Anatoliy Malyarenko
Publisher : Springer Nature
Page : 833 pages
File Size : 45,8 Mb
Release : 2023-09-25
Category : Mathematics
ISBN : 9783031320095

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Non-commutative and Non-associative Algebra and Analysis Structures by Sergei Silvestrov,Anatoliy Malyarenko Pdf

The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Västerås, Sweden, from September 30th to October 2nd 2019 was to showcase the frontiers of research in several important topics of mathematics, mathematical statistics, and its applications. The conference has been organized along the following tracks: 1. Stochastic processes and modern statistical methods in theory and practice, 2. Engineering Mathematics, 3. Algebraic Structures and applications. This book highlights the latest advances in algebraic structures and applications focused on mathematical notions, methods, structures, concepts, problems, algorithms, and computational methods for the natural sciences, engineering, and modern technology. In particular, the book features mathematical methods and models from non-commutative and non-associative algebras and rings associated to generalizations of differential calculus, quantum deformations of algebras, Lie algebras, Lie superalgebras, color Lie algebras, Hom-algebras and their n-ary generalizations, semi-groups and group algebras, non-commutative and non-associative algebras and computational algebra interplay with q-special functions and q-analysis, topology, dynamical systems, representation theory, operator theory and functional analysis, applications of algebraic structures in coding theory, information analysis, geometry and probability theory. The book gathers selected, high-quality contributed chapters from several large research communities working on modern algebraic structures and their applications. The chapters cover both theory and applications, and are illustrated with a wealth of ideas, theorems, notions, proofs, examples, open problems, and results on the interplay of algebraic structures with other parts of Mathematics. The applications help readers grasp the material, and encourage them to develop new mathematical methods and concepts in their future research. Presenting new methods and results, reviews of cutting-edge research, open problems, and directions for future research, will serve as a source of inspiration for a broad range of researchers and students.

Author : Bernard Russo,Asuman Güven Aksoy,Ravshan Ashurov,Shavkat Ayupov
Publisher : American Mathematical Soc.
Page : 272 pages
File Size : 41,6 Mb
Release : 2016-08-25
Category : Banach algebras
ISBN : 9781470419288

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Topics in Functional Analysis and Algebra by Bernard Russo,Asuman Güven Aksoy,Ravshan Ashurov,Shavkat Ayupov Pdf

The USA-Uzbekistan Conference on Analysis and Mathematical Physics, focusing on contemporary issues in dynamical systems, mathematical physics, operator algebras, and several complex variables, was hosted by California State University, Fullerton, from May 20–23, 2014. The main objective of the conference was to facilitate scientific communication and collaboration between mathematicians from the USA and Uzbekistan. This volume contains the proceedings of the Special Session on Algebra and Functional Analysis. The theory of operator algebras is the unified theme for many papers in this volume. Out of four extensive survey papers, two cover problems related to derivation of various algebras of functions. The other two surveys are on classification of Leibniz algebras and on evolution algebras. The sixteen research articles are devoted to certain analytic topics, such as minimal projections with respect to numerical radius, functional equations and discontinuous polynomials, Fourier inversion for distributions, Schrödinger operators, convexity and dynamical systems.

Author : Leonid Kurdachenko
Publisher : Springer Nature
Page : 173 pages
File Size : 44,7 Mb
Release : 2024-07-03
Category : Electronic
ISBN : 9783031581489

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General Theory of Leibniz Algebras by Leonid Kurdachenko Pdf

Author : Petr Vojtěchovský,Murray R. Bremner,J. Scott Carter,Anthony B. Evans,John Huerta,Michael K. Kinyon,G. Eric Moorhouse,Jonathan D. H. Smith
Publisher : American Mathematical Soc.
Page : 297 pages
File Size : 55,8 Mb
Release : 2019-01-14
Category : Nonassociative algebras
ISBN : 9781470442453

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Nonassociative Mathematics and its Applications by Petr Vojtěchovský,Murray R. Bremner,J. Scott Carter,Anthony B. Evans,John Huerta,Michael K. Kinyon,G. Eric Moorhouse,Jonathan D. H. Smith Pdf

Nonassociative mathematics is a broad research area that studies mathematical structures violating the associative law x(yz)=(xy)z. The topics covered by nonassociative mathematics include quasigroups, loops, Latin squares, Lie algebras, Jordan algebras, octonions, racks, quandles, and their applications. This volume contains the proceedings of the Fourth Mile High Conference on Nonassociative Mathematics, held from July 29–August 5, 2017, at the University of Denver, Denver, Colorado. Included are research papers covering active areas of investigation, survey papers covering Leibniz algebras, self-distributive structures, and rack homology, and a sampling of applications ranging from Yang-Mills theory to the Yang-Baxter equation and Laver tables. An important aspect of nonassociative mathematics is the wide range of methods employed, from purely algebraic to geometric, topological, and computational, including automated deduction, all of which play an important role in this book.

Author : Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov
Publisher : American Mathematical Society
Page : 296 pages
File Size : 47,8 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9780821898529

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Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics by Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov Pdf

This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Author : Ana Agore,Gigel Militaru
Publisher : CRC Press
Page : 243 pages
File Size : 44,9 Mb
Release : 2019-08-29
Category : Mathematics
ISBN : 9781351168717

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Extending Structures by Ana Agore,Gigel Militaru Pdf

Extending Structures: Fundamentals and Applications treats the extending structures (ES) problem in the context of groups, Lie/Leibniz algebras, associative algebras and Poisson/Jacobi algebras. This concisely written monograph offers the reader an incursion into the extending structures problem which provides a common ground for studying both the extension problem and the factorization problem. Features Provides a unified approach to the extension problem and the factorization problem Introduces the classifying complements problem as a sort of converse of the factorization problem; and in the case of groups it leads to a theoretical formula for computing the number of types of isomorphisms of all groups of finite order that arise from a minimal set of data Describes a way of classifying a certain class of finite Lie/Leibniz/Poisson/Jacobi/associative algebras etc. using flag structures Introduces new (non)abelian cohomological objects for all of the aforementioned categories As an application to the approach used for dealing with the classification part of the ES problem, the Galois groups associated with extensions of Lie algebras and associative algebras are described

Author : Jean-Louis Loday
Publisher : American Mathematical Soc.
Page : 458 pages
File Size : 41,7 Mb
Release : 1997
Category : Electronic
ISBN : 9780821805138

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Operads: Proceedings of Renaissance Conferences by Jean-Louis Loday Pdf

Author : Y. Khakimdjanov,M. Goze,Sh. Ayupov
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 45,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401150729

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Algebra and Operator Theory by Y. Khakimdjanov,M. Goze,Sh. Ayupov Pdf

This volume presents the lectures given during the second French-Uzbek Colloquium on Algebra and Operator Theory which took place in Tashkent in 1997, at the Mathematical Institute of the Uzbekistan Academy of Sciences. Among the algebraic topics discussed here are deformation of Lie algebras, cohomology theory, the algebraic variety of the laws of Lie algebras, Euler equations on Lie algebras, Leibniz algebras, and real K-theory. Some contributions have a geometrical aspect, such as supermanifolds. The papers on operator theory deal with the study of certain types of operator algebras. This volume also contains a detailed introduction to the theory of quantum groups. Audience: This book is intended for graduate students specialising in algebra, differential geometry, operator theory, and theoretical physics, and for researchers in mathematics and theoretical physics.

Author : Adem Kilicman,Wah June Leong,Zainidin Eshkuvatov
Publisher : Springer Science & Business Media
Page : 286 pages
File Size : 48,6 Mb
Release : 2014-03-16
Category : Mathematics
ISBN : 9789814585330

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International Conference on Mathematical Sciences and Statistics 2013 by Adem Kilicman,Wah June Leong,Zainidin Eshkuvatov Pdf

This volume is devoted to the most recent discoveries in mathematics and statistics. It also serves as a platform for knowledge and information exchange between experts from industrial and academic sectors. The book covers a wide range of topics, including mathematical analyses, probability, statistics, algebra, geometry, mathematical physics, wave propagation, stochastic processes, ordinary and partial differential equations, boundary value problems, linear operators, cybernetics and number and functional theory. It is a valuable resource for pure and applied mathematicians, statisticians, engineers and scientists.

Author : V. Futorny
Publisher : American Mathematical Soc.
Page : 299 pages
File Size : 51,8 Mb
Release : 2009
Category : Mathematics
ISBN : 9780821846520

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Algebras, Representations and Applications by V. Futorny Pdf

This volume contains contributions from the conference on "Algebras, Representations and Applications" (Maresias, Brazil, August 26-September 1, 2007), in honor of Ivan Shestakov's 60th birthday. The collection of papers presented here is of great interest to graduate students and researchers working in the theory of Lie and Jordan algebras and superalgebras and their representations, Hopf algebras, Poisson algebras, Quantum Groups, Group Rings and other topics.