A quantum groups primer [E-Book] / Shahn Majid.
Majid, Shahn, (author)
Cambridge : Cambridge University Press, 2002
1 online resource (x, 169 pages)
englisch
9780511549892
9780521010412
London Mathematical Society lecture note series ; 292
Full Text
Table of 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.