UID:
almahu_9948233996702882
Format:
1 online resource (x, 169 pages) :
,
digital, PDF file(s).
ISBN:
9780511549892 (ebook)
Series Statement:
London Mathematical Society lecture note series ; 292
Content:
This book provides a self-contained introduction to quantum groups as algebraic objects. Based on the author's lecture notes from a Part III pure mathematics course at Cambridge University, it is suitable for use as a textbook for graduate courses in quantum groups or as a supplement to modern courses in advanced algebra. The book assumes a background knowledge of basic algebra and linear algebra. Some familiarity with semisimple Lie algebras would also be helpful. The book is aimed as a primer for mathematicians and takes a modern approach leading into knot theory, braided categories and noncommutative differential geometry. It should also be useful for mathematical physicists.
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
,
Coalgebras, bialgebras and Hopf algebras. Uq(b+) -- Dual pairing. SLq(2). Actions -- Coactions. Quantum plane A2q -- Automorphism quantum groups -- Quasitriangular structures -- Roots of Unity. uq(sl2) -- q-Binomials -- Quantum double. Dual-quasitriangular structures -- Braided categories -- (Co)module categories. Crossed modules -- q-Hecke algebras -- Rigid objects. Dual representations. Quantum dimension -- Knot invariants -- Hopf algebras in braided categories -- Braided differentiation -- Bosonisation. Inhomogeneous quantum groups -- Double bosonisation. Diagrammatic construction of uq(sl2) -- The braided group Uq(n- ). Construction of Uq(g) -- q-Serre relations -- R-matrix methods -- Group algebra, Hopf algebra factorisations. Bicrossproducts -- Lie bialgebras. Lie splittings. Iwasawa decomposition -- Poisson geometry. Noncommutative bundles. q-Sphere -- Connections. q-Monopole. Nonuniversal differentials.
Additional Edition:
Print version: ISBN 9780521010412
Language:
English
Subjects:
Mathematics
URL:
https://doi.org/10.1017/CBO9780511549892
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