Non-commutative and non-associative algebra and analysis structures : SPAS 2019, Västerås, Sweden, September 30-October 2 / Sergei Silvestrov, Anatoliy Malyarenko, editors.
SPAS (Conference) (2019 : Västerås, Sweden); Silvestrov, Sergei D.; Malyarenko, Anatoliy.
2023
QA274.A1 S63 2017
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Title Non-commutative and non-associative algebra and analysis structures : SPAS 2019, Västerås, Sweden, September 30-October 2 / Sergei Silvestrov, Anatoliy Malyarenko, editors.
Meeting Name SPAS (Conference) (2019 : Västerås, Sweden)
ISBN 9783031320095 (electronic bk.)
3031320093 (electronic bk.)
3031320085
9783031320088
DOI https://doi.org/10.1007/978-3-031-32009-5
Publication Details Cham : Springer, 2023.
Language English
Description 1 online resource (833 p.).
Item Number 10.1007/978-3-031-32009-5 doi
Call Number QA274.A1 S63 2017
Dewey Decimal Classification 519.2
Summary The goal of the 2019 conference on Stochastic Processes and Algebraic Structures held in SPAS2019, Vsters, 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.
Note 8.3.3 Quaternion-Spectral Equivalence
Includes indexes.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed October 12, 2023).
Added Author Silvestrov, Sergei D.
Malyarenko, Anatoliy.
Series Springer proceedings in mathematics & statistics ; v. 426.
Available in Other Form Non-Commutative and Non-associative Algebra and Analysis Structures
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Intro
Preface
Contents
Contributors
1 Index of Hom-Lie Algebras
1.1 Introduction
1.2 Preliminary
1.2.1 Hom-Lie Algebras
1.2.2 Representations of Hom-Lie Algebras
1.3 Index of Hom-Lie Algebras
1.3.1 For a Coadjoint Representation
1.3.2 For an Arbitrary Representation
1.3.3 Index of Twisted Lie Algebras
1.3.4 Index of Multiplicative Simple Hom-Lie Algebras
1.4 Index of Semidirect Products of Hom-Lie Algebras
1.4.1 Coadjoint Representations
1.4.2 The Stabilizer of an Arbitrary Point of mathfrakqast
References

2 On Ternary (Hom-)Nambu-Poisson Algebras
2.1 Introduction
2.2 Ternary Nambu-Poisson Algebras Induced by Poisson Algebras
2.2.1 Examples
2.2.2 Constructing Poisson and Ternary Nambu-Poisson Algebras from Solvable Lie Algebras
2.3 Ternary Hom-Nambu-Poisson Algebras Induced by Hom-Poisson Algebras
2.3.1 Examples
References
3 Classification, Centroids and Derivations of Two-Dimensional Hom-Leibniz Algebras
3.1 Introduction
3.2 Hom-Leibniz Algebras and Superalgebras
3.3 Symmetric (Two-Sided) Hom-Leibniz Superalgebras

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