Title: Hopf algebras and Quantum groups

Lecturer: Marc Rosso, Université Denis Diderot - Paris VII

Time: 9:00 -- 12:00 on May 12, 14:00 -- 17:00 on May 13, 9:00 -- 10:30 on May 26 and June 2, 14:00 -- 15:30 on May 27 and June 3.

Place: Room 1328 at BICMR, Resource Plaza, Peking University on May 12, May 26 and June 2 and room 1218 at BICMR, Resource Plaza, Peking University on May 13, May 27 and June 3.

Description:

• 1. Hopf algebras:
  Definitions, examples, general properties. Modules, comodules, Hopf bimodules and their structural properties.
• 2.Yang-Baxter Equation:
  Almost cocommutative Hopf algebras, quasi-triangular Hopf algebras, Yang-Baxter equation. Quantum double construction and examples. Connection with braid groups and braided tensor categories.
• 3. Quantized enveloping algebras:
  Constructions of quantized enveloping algebras associated with a symmetrizable Cartan matrix. Representations. Universal R-matrix and concrete solutions of the Yang-Baxter equation. Quantum Schur-Weyl duality.
• 4. Applications to invariants of links:
  Markov traces and general construction of link invariants. Examples of the Jones polynomial and Homfly polynomial.
• 5. (If time permits) Quantized enveloping algebras at a root of unity.