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Half-quantum groups at roots of unity, path algebras and representation type

Claude Cibils
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Abstract

We show that finite dimensional half-quantum groups at roots of unity corresponding to simple Lie algebras having symmetric Cartan matrix are of wild representation type, except for sl_2. Moreover, the underlying associative algebra is isomorphic to an admissible quotient of the path algebra of the Cayley graph of an abelian group. A quantum type Fourier transform enables to describe an explicit isomorphism.

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Claude Cibils. 1997-02-03. Half-quantum groups at roots of unity, path algebras and representation type. https://arxiv.org/abs/q-alg/9702005

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