Overview

The aim of this book is to extend the understanding of the fundamental role of generalizations of Lie and related non-commutative and non-associative structures in Mathematics and Physics. This is a thematic volume devoted to the interplay between several rapidly exp- ding research ?elds in contemporary Mathematics and Physics, such as generali- tions of the main structures of Lie theory aimed at quantization and discrete and non-commutative extensions of differential calculus and geometry, non-associative structures, actions of groups and semi-groups, non-commutative dynamics, n- commutative geometry and applications in Physics and beyond. The speci?c ?elds covered by this volume include: * Applications of Lie, non-associative and non-commutative associative structures to generalizations of classical and quantum mechanics and non-linear integrable systems, operadic and group theoretical methods; * Generalizations and quasi-deformations of Lie algebras such as color and super Lie algebras, quasi-Lie algebras, Hom-Lie algebras, in?nite-dimensional Lie algebras of vector ?elds associated to Riemann surfaces, quasi-Lie algebras of Witt type and their central extensions and deformations important for in- grable systems, for conformal ? eld theory and for string theory; * Non-commutative deformation theory, moduli spaces and interplay with n- commutativegeometry,algebraicgeometryandcommutativealgebra,q-deformed differential calculi and extensions of homological methods and structures; * Crossed product algebras and actions of groups and semi-groups, graded rings and algebras, quantum algebras, twisted generalizations of coalgebras and Hopf algebra structures such as Hom-coalgebras, Hom-Hopf algebras, and super Hopf algebras and their applications to bosonisation, parastatistics, parabosonic and parafermionic algebras, orthoalgebas and root systems in quantum mechanics;

Full Product Details

Author:   Sergei D. Silvestrov ,  Eugen Paal ,  Viktor Abramov ,  Alexander Stolin
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   Softcover reprint of hardcover 1st ed. 2009
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.012kg
ISBN:  

9783642099045

ISBN 10:   3642099041
Pages:   306
Publication Date:   19 October 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Non-Associative and Non-Commutative Structures for Physics.- Moufang Transformations and Noether Currents.- Weakly Nonassociative Algebras, Riccati and KP Hierarchies.- Applications of Transvectants.- Automorphisms of Finite Orthoalgebras, Exceptional Root Systems and Quantum Mechanics.- A Rewriting Approach to Graph Invariants.- Non-Commutative Deformations, Quantization, Homological Methods, and Representations.- Graded q-Differential Algebra Approach to q-Connection.- On Generalized N-Complexes Coming from Twisted Derivations.- Remarks on Quantizations, Words and R-Matrices.- Connections on Modules over Singularities of Finite and Tame CM Representation Type.- Computing Noncommutative Global Deformations Of D-Modules.- Comparing Small Orthogonal Classes.- Groups and Actions.- How to Compose Lagrangian?.- Semidirect Products of Generalized Quaternion Groups by a Cyclic Group.- A Characterization Of A Class Of 2-Groups By Their Endomorphism Semigroups.- Adjoint Representations and Movements.- Applications of Hypocontinuous Bilinear Maps in Infinite-Dimensional Differential Calculus.- Quasi-Lie, Super-Lie, Hom-Hopf and Super-Hopf Structures and Extensions, Deformations and Generalizations of Infinite-Dimensional Lie Algebras.- Hom-Lie Admissible Hom-Coalgebras and Hom-Hopf Algebras.- Bosonisation and Parastatistics.- Deformations of the Witt, Virasoro, and Current Algebra.- Conformal Algebras in the Context of Linear Algebraic Groups.- Lie Color and Hom-Lie Algebras of Witt Type and Their Central Extensions.- A Note on Quasi-Lie and Hom-Lie Structures of ?-Derivations of C=[Z 1 ±1 ,…,Z n ±1 ].- Commutative Subalgebras in Noncommutative Algebras.- Algebraic Dependence of Commuting Elements in Algebras.- Crossed Product-Like and Pre-Crystalline Graded Rings.-Decomposition of the Enveloping Algebra so(5).

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