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 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.

14 pages, Latex. http://www.unige.ch/math/folks/cibils/apublics.html