arXiv subjects
Publications and source records attributed to Christian Ohn.
We study the only missing case in the classification of quantum SL(3,C)'s undertaken in our paper [J. of Algebra 213 (1999), 721--756; see http://arxiv.org/abs/q-alg/9711005], thereby completing this classification.
We suggest a possible programme to associate geometric "flag-like" data to an arbitrary simple quantum group, in the spirit of the noncommutative algebraic geometry developed by Artin, Tate, and Van den Bergh. We then carry out this programme for the standard quantum SL(n) of Drinfel'd and Jimbo, where the varieties involved are certain T-stable subvarieties of the (ordinary) flag variety.
Let G be a connected complex semi-simple group, B a Borel subgroup of G, and T a maximal torus in B. We construct a class of smooth T-stable subvarieties inside the flag variety G/B, each of which is an embedding of a product of projective lines.
We study and classify almost all quantum SL(3,C)'s whose representation theory is ``similar'' to that of the (ordinary) group SL(3,C). Only one case, related to smooth elliptic curves, could not be treated completely.