Quantum Double and Differential Calculi
q-alg
2009-10-28 v2 量子代数
摘要
We show that bicovariant bimodules as defined by Woronowicz are in one to one correspondence with the Drinfeld quantum double representations. We then prove that a differential calculus associated to a bicovariant bimodule of dimension n is connected to the existence of a particular (n+1)--dimensional representation of the double. An example of bicovariant differential calculus on the non quasitriangular quantum group E_q(2) is developed. The construction is studied in terms of Hochschild cohomology and a correspondence between differential calculi and 1-cocycles is proved. Some differences of calculi on quantum and finite groups with respect to Lie groups are stressed.
引用
@article{arxiv.q-alg/9507004,
title = {Quantum Double and Differential Calculi},
author = {F. Bonechi and R. Giachetti and R. Maciocco and E. Sorace and M. Tarlini},
journal= {arXiv preprint arXiv:q-alg/9507004},
year = {2009}
}
备注
Revised version with added cohomological analysis. 14 pages, plain tex