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Generalized Lie Theory in Mathematics, Physics and Beyond by Eugen Paal (2010, Trade Paperback)

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Generalized Lie Theory in Mathematics, Physics and Beyond by Sergei D. Silvestrov, Eugen Paal, Viktor Abramov, Alexander Stolin. The speci?c ?. elds associated to Riemann surfaces, quasi-Lie algebras of Witt type and their central extensions and deformations important for in- grable systems, for conformal ?.

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Product Information

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;

Product Identifiers

Publisher
Springer Berlin / Heidelberg
ISBN-10
3642099041
ISBN-13
9783642099045
eBay Product ID (ePID)
109126794

Product Key Features

Author
Eugen Paal
Publication Name
Generalized Lie Theory in Mathematics, Physics and Beyond
Format
Trade Paperback
Language
English
Publication Year
2010
Type
Textbook
Number of Pages
Xviii, 306 Pages

Dimensions

Item Length
9.3in
Item Width
6.1in
Item Weight
35.7 Oz

Additional Product Features

Number of Volumes
1 Vol.
Lc Classification Number
Qa150-272
Table of Content
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).
Copyright Date
2009
Target Audience
Scholarly & Professional
Topic
Group Theory, Algebra / General, Physics / Mathematical & Computational
Dewey Decimal
512.482
Dewey Edition
22
Illustrated
Yes
Genre
Science, Mathematics

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Generalized Lie Theory in Mathematics, Physics and Beyond by Eugen Paal (2010, Trade Paperback)

About this product

Product Information

Product Identifiers

Product Key Features

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Additional Product Features

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