Extensions of finite quantum groups by finite groups

NICOLÁS ANDRUSKIEWITSCH Y GASTÓN ANDRÉS GARCÍA

En revisión para enviar a publicar.

Año: 2006 p. 1 - 37

Let G be a connected, simply connected complex semisimple Liegroup with Lie algebra g, Cartan matrix C and symmetrizedCartan matrix CD. Let N > 1 be an odd integer, relativelyprime to det CD. Given an embedding {sigma} of a finite groupH on G and a primitive N-th root of unity {epsilon}, weconstruct a central extension A_{sigma} of the function algebraC^{H} by the dual of the Frobenius-Lusztig kernel;A_{sigma} is a quotient of the quantized coordinate algebra of Gand dim A_{sigma} =|H|N^{dim g}. LetC_{G}(sigma(H)) be the centralizer of {sigma}(H) in G. IfG is simple and dim C_{G}(sigma(H)) < dim G - rg G, thenwe obtain an infinite family of pairwise non-isomorphic Hopfalgebras which are non-semisimple and non-pointed; under certaincondition, their duals are non-pointed. This generalizes the resultobtained by E. Müller for SL_{2}(C).