Generalized Lie Theory in Mathematics, Physics and Beyond

by Sergei Silvestrov (Editor), Eugen Paal (Editor), Viktor Abramov (Editor)

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 - 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;

324 pages, Hardcover

First published November 1, 2008

Reviews

[Theresa Leone Davidson · Rating 4 out of 5]

Didn't care for math in high school and usually took the lazy way out, not challenging myself, but in college I was inspired by wonderful professors who taught me, among other things, the beauty of mathematics and physics, so I read this, although I suspect it would be more useful to someone who is involved in either discipline professionally. The theory given, which was developed initially by a man named Sophus Lie, is fascinating, and how it ties in to both math and physics I found to be interesting. Some aspects of Lie's theory have been challenged in recent years but that's discussed in the book, too, and while I have not studied either physics or any branch of mathematics in many years, I didn't feel that the material was over my head. A great read if you like the subject.