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The geometric reductivity of the quantum group S L q ( 2 )

Michał Kępa, Andrzej Tyc (2011)

Colloquium Mathematicae

We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants A G is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...

Weak multiplier Hopf algebras. Preliminaries, motivation and basic examples

Alfons Van Daele, Shuanhong Wang (2012)

Banach Center Publications

Let G be a finite group. Consider the algebra A of all complex functions on G (with pointwise product). Define a coproduct Δ on A by Δ(f)(p,q) = f(pq) where f ∈ A and p,q ∈ G. Then (A,Δ) is a Hopf algebra. If G is only a groupoid, so that the product of two elements is not always defined, one still can consider A and define Δ(f)(p,q) as above when pq is defined. If we let Δ(f)(p,q) = 0 otherwise, we still get a coproduct on A, but Δ(1) will no longer be the identity in A ⊗ A. The pair (A,Δ)...

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