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Books > Science & Mathematics > Mathematics > Algebra
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Generalized Lie Theory in Mathematics, Physics and Beyond (Hardcover, 2009 ed.)
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Generalized Lie Theory in Mathematics, Physics and Beyond (Hardcover, 2009 ed.)
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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;
General
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