Generalized Lie Theory in Mathematics, Physics and Beyond

• Corporate Author: SpringerLink (Online service)
• Other Authors: Silvestrov, Sergei (Editor), Paal, Eugen (Editor), Abramov, Viktor (Editor), Stolin, Alexander (Editor)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2009.
• Subjects: Mathematics.; Algebra.; Topological groups.; Lie groups.; Physics.; Topological Groups, Lie Groups.; Theoretical, Mathematical and Computational Physics.

The goal of this book is to extend the understanding of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics. This volume is devoted to the interplay between several rapidly expanding research fields in contempora...

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).