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A quantum groups primer / Shahn Majid.
- Format:
- Book
- Author/Creator:
- Majid, Shahn, author.
- Series:
- London Mathematical Society lecture note series ; 292.
- London Mathematical Society lecture note series ; 292
- Language:
- English
- Subjects (All):
- Quantum groups.
- Physical Description:
- 1 online resource (x, 169 pages) : digital, PDF file(s).
- Place of Publication:
- Cambridge : Cambridge University Press, 2002.
- Language Note:
- English
- Summary:
- 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.
- Contents:
- 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.
- Notes:
- Title from publisher's bibliographic system (viewed on 05 Oct 2015).
- Includes bibliographical references and index.
- ISBN:
- 1-139-88142-6
- 1-107-36566-X
- 1-107-37040-X
- 1-107-36075-7
- 1-107-37023-X
- 1-299-40348-4
- 1-107-36320-9
- 0-511-54989-X
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