Lectures on Quantum Groups by Olivier Schiffman, Pavel Etingof

By Olivier Schiffman, Pavel Etingof

Revised moment variation. The textual content covers the fabric awarded for a graduate-level direction on quantum teams at Harvard college. The contents hide: Poisoon algebras and quantization, Poisson-Lie teams, coboundary Lie bialgebras, Drinfelds double building, Belavin-Drinfeld class, endless dimensional Lie bialgebras, Hopf algebras, Quantized common enveloping algebras, formal teams and h-formal teams, endless dimensional quantum teams, the quantum double, tensor different types and quasi Hopf-algebras, braided tensor different types, KZ equations and the Drinfeld type, Quasi-Hpf enveloping algebras, Lie associators, Fiber functors and Tannaka-Driein duality, Quantization of finite Lie bialgebras, common structures, common quantization, Dequantization and the equivalence theorem, KZ associator and a number of zeta services, and Mondoromy of trigonometric KZ equations. Probems are given with every one topic and a solution secret is integrated. desk of contents Poisson algebras and quantization Poisson-Lie teams Coboundary Lie bialgebras Drinfeld's double development Belavin-Drinfeld category (I) countless dimensional Lie bialgebras Belavin-Drinfeld class (II) Hopf algebras Quantized common enveloping algebras Formal teams and h-formal teams limitless dimensional quantum teams The quantum double Tensor different types and quasi-Hopfalgebras Braided tensor different types KZ equations and the Drinfeld classification Quasi-Hopf quantized enveloping algebras Lie associators Fiber functors and Tannaka-Krein duality Quantization of finite dimensional Lie bialgebras common structures common quantization Dequantization and the Equalivalence

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Rd n).

Show that if N is a left R-module then as an abelian group S ⊗R N ∼ = N d with isomorphism induced from (s1 r1 + · · · + sd rd ) ⊗ n = si ⊗ (ri n) → (r1 n, r2 n, . . rd n).

Sd . Show that if N is a left R-module then as an abelian group S ⊗R N ∼ = N d with isomorphism induced from (s1 r1 + · · · + sd rd ) ⊗ n = si ⊗ (ri n) → (r1 n, r2 n, . . rd n).

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