Twisted derivations of Hopf algebras
Quantum Algebra
2012-04-24 v1
Abstract
In the paper we introduce the notion of twisted derivation of a bialgebra. Twisted derivations appear as infinitesimal symmetries of the category of representations. More precisely they are infinitesimal versions of twisted automorphisms of bialgebras. Twisted derivations naturally form a Lie algebra (the tangent algebra of the group of twisted automorphisms). Moreover this Lie algebra fits into a crossed module (tangent to the crossed module of twisted automorphisms). Here we calculate this crossed module for universal enveloping algebras and for the Sweedler's Hopf algebra.
Keywords
Cite
@article{arxiv.1204.4828,
title = {Twisted derivations of Hopf algebras},
author = {Alexei Davydov},
journal= {arXiv preprint arXiv:1204.4828},
year = {2012}
}