  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.

Quantum Algebra