Twisted derivations of Hopf algebras

Details Twisted derivations of Hopf algebras Twisted derivations of Hopf algebras

2012-04-21

arxiv.org/abs/1204.4828v1

Mathematics

Quantum Algebra

Scientific paper

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.

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