Derivations and other inductive operator families

Abstract: Derivations on group algebras are linear operators. They satisfy the Leibniz rule. Another example are Fox derivatives, which satisfy a different (but very similar) identity. We will give a construction which generalises all such identities and the corresponding operator families. The main element of such a construction is an action groupoid and the space ofcharacters on it. The second step of the construction are characters on special graphs (action diagrams) which are equivalent to classical Cayley graphs for the case of left multiplication action. I will show the way to interpret inner derivations as a special case of trivial on loops characters. And we will consider a more general ideal of quasi-inner derivations. These results are based on the author's results, and the main approach was proposed in collaboration with prof. A. S. Mischchenko.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar