Half-quantum groups at roots of unity, path algebras and representation type
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 sl2. 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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