Non Commutative And Non Associative Algebra And Analysis Structures

Author : Sergei Silvestrov,Anatoliy Malyarenko
Publisher : Springer Nature
Page : 833 pages
File Size : 46,5 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 : Lev Sabinin,Larissa Sbitneva,Ivan Shestakov
Publisher : CRC Press
Page : 553 pages
File Size : 52,7 Mb
Release : 2006-01-13
Category : Mathematics
ISBN : 9781420003451

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Non-Associative Algebra and Its Applications by Lev Sabinin,Larissa Sbitneva,Ivan Shestakov Pdf

With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.

Author : Mercedes Siles Molina,Laiachi El Kaoutit,Mohamed Louzari,L'Moufadal Ben Yakoub,Mohamed Benslimane
Publisher : Springer Nature
Page : 338 pages
File Size : 51,6 Mb
Release : 2020-01-02
Category : Mathematics
ISBN : 9783030352561

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Associative and Non-Associative Algebras and Applications by Mercedes Siles Molina,Laiachi El Kaoutit,Mohamed Louzari,L'Moufadal Ben Yakoub,Mohamed Benslimane Pdf

This book gathers together selected contributions presented at the 3rd Moroccan Andalusian Meeting on Algebras and their Applications, held in Chefchaouen, Morocco, April 12-14, 2018, and which reflects the mathematical collaboration between south European and north African countries, mainly France, Spain, Morocco, Tunisia and Senegal. The book is divided in three parts and features contributions from the following fields: algebraic and analytic methods in associative and non-associative structures; homological and categorical methods in algebra; and history of mathematics. Covering topics such as rings and algebras, representation theory, number theory, operator algebras, category theory, group theory and information theory, it opens up new avenues of study for graduate students and young researchers. The findings presented also appeal to anyone interested in the fields of algebra and mathematical analysis.

Author : Florin Felix Nichita
Publisher : MDPI
Page : 106 pages
File Size : 40,7 Mb
Release : 2020-06-16
Category : Mathematics
ISBN : 9783039362547

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Non-associative Structures and Other Related Structures by Florin Felix Nichita Pdf

Leonhard Euler (1707–1783) was born in Basel, Switzerland. Euler's formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential function. When its variable is the number pi, Euler's formula evaluates to Euler's identity. On the other hand, the Yang–Baxter equation is considered the most beautiful equation by many scholars. In this book, we study connections between Euler’s formulas and the Yang–Baxter equation. Other interesting sections include: non-associative algebras with metagroup relations; branching functions for admissible representations of affine Lie Algebras; super-Virasoro algebras; dual numbers; UJLA structures; etc.

Author : Richard D. Schafer
Publisher : Courier Dover Publications
Page : 176 pages
File Size : 46,5 Mb
Release : 2017-11-15
Category : Mathematics
ISBN : 9780486164175

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An Introduction to Nonassociative Algebras by Richard D. Schafer Pdf

Concise graduate-level introductory study presents some of the important ideas and results in the theory of nonassociative algebras. Places particular emphasis on alternative and (commutative) Jordan algebras. 1966 edition.

Author : Linsen Chou
Publisher : Unknown
Page : 0 pages
File Size : 50,6 Mb
Release : 2015-08
Category : Electronic
ISBN : 1681171880

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Introduction to Noncommutative Algebra by Linsen Chou Pdf

A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. The main motivation is to extend the commutative duality between spaces and functions to the noncommutative setting. In mathematics, spaces, which are geometric in nature, can be related to numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many cases, we can recover X from C(X), and therefore it makes some sense to say that X has commutative topology. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras, or sheaf-like noncommutative algebraic or operator-algebraic structures and geometric entities of certain kind, and interact between the algebraic and geometric description of those via this duality. Regarding that the commutative rings correspond to usual affine schemes, and commutative C*-algebras to usual topological spaces, the extension to noncommutative rings and algebras requires non-trivial generalization of topological spaces, as "non-commutative spaces". This book provides an elementary introduction to noncommutative rings and algebras.

Author : Cheikh Thiécoumbe Gueye,Mercedes Siles Molina
Publisher : Springer
Page : 254 pages
File Size : 45,9 Mb
Release : 2016-11-21
Category : Mathematics
ISBN : 9783319329024

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Non-Associative and Non-Commutative Algebra and Operator Theory by Cheikh Thiécoumbe Gueye,Mercedes Siles Molina Pdf

Presenting the collaborations of over thirty international experts in the latest developments in pure and applied mathematics, this volume serves as an anthology of research with a common basis in algebra, functional analysis and their applications. Special attention is devoted to non-commutative algebras, non-associative algebras, operator theory and ring and module theory. These themes are relevant in research and development in coding theory, cryptography and quantum mechanics. The topics in this volume were presented at the Workshop on Non-Associative & Non-Commutative Algebra and Operator Theory, held May 23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honor of Professor Amin Kaidi. The workshop was hosted by the university's Laboratory of Algebra, Cryptology, Algebraic Geometry and Applications, in cooperation with the University of Almería and the University of Málaga. Dr. Kaidi's work focuses on non-associative rings and algebras, operator theory and functional analysis, and he has served as a mentor to a generation of mathematicians in Senegal and around the world.

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 364 pages
File Size : 46,7 Mb
Release : 2017-04-11
Category : Mathematics
ISBN : 9781351869874

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Algebras, Rings and Modules, Volume 2 by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This is the second volume of Algebras, Rings and Modules: Non-commutative Algebras and Rings by M. Hazewinkel and N. Gubarenis, a continuation stressing the more important recent results on advanced topics of the structural theory of associative algebras, rings and modules.

Author : Helena Albuquerque,Jose Brox,Consuelo Martínez,Paulo Saraiva
Publisher : Springer Nature
Page : 305 pages
File Size : 41,5 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 : F.M.J. van Oystaeyen,A.H.M.J. Verschoren
Publisher : Springer
Page : 408 pages
File Size : 45,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540386018

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Non-commutative Algebraic Geometry by F.M.J. van Oystaeyen,A.H.M.J. Verschoren Pdf

Author : Robert George Hathway
Publisher : Unknown
Page : 162 pages
File Size : 45,5 Mb
Release : 1966
Category : Algebra, Abstract
ISBN : WISC:89010967834

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On Non-commutative Non-associative Algebras by Robert George Hathway Pdf

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 388 pages
File Size : 49,9 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482245059

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Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Author : I. N. Herstein
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 49,5 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 9780883850152

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Noncommutative Rings by I. N. Herstein Pdf

Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.

Author : Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima
Publisher : Springer Science & Business Media
Page : 496 pages
File Size : 45,9 Mb
Release : 1993-11-30
Category : Science
ISBN : 079232532X

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Quantum and Non-Commutative Analysis by Huzihiro Araki,Keiichi R. Ito,Akitaka Kishimoto,Izumi Ojima Pdf

In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc. on the side of mathematics, quantum field theory and statistical mechanics on the side of mathematical physics. The new development is characterized by very strong relations and interactions between different research areas which were hitherto considered as remotely related. Focussing on these new developments in mathematical physics and theory of operator algebras, the International Oji Seminar on Quantum Analysis was held at the Kansai Seminar House, Kyoto, JAPAN during June 25-29, 1992 by a generous sponsorship of the Japan Society for the Promotion of Science and the Fujihara Foundation of Science, as a workshop of relatively small number of (about 50) invited participants. This was followed by an open Symposium at RIMS, described below by its organizer, A. Kishimoto. The Oji Seminar began with two key-note addresses, one by V.F.R. Jones on Spin Models in Knot Theory and von Neumann Algebras and by A. Jaffe on Where Quantum Field Theory Has Led. Subsequently topics such as Subfactors and Sector Theory, Solvable Models of Statistical Mechanics, Quantum Field Theory, Quantum Groups, and Renormalization Group Ap proach, are discussed. Towards the end, a panel discussion on Where Should Quantum Analysis Go? was held.

Author : Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić
Publisher : Springer Nature
Page : 976 pages
File Size : 42,8 Mb
Release : 2020-06-18
Category : Mathematics
ISBN : 9783030418502

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Algebraic Structures and Applications by Sergei Silvestrov,Anatoliy Malyarenko,Milica Rančić Pdf

This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas.