E(n)-coactions on semisimple Clifford algebras

Abstract

In this article we prove that $E(n)$-coactions over a finite-dimensional algebra $A$ are classified by tuples $(\ddot{I}†,d_1,...,d_n)$ consisting of an involution $\ddot{I}†$ and a family $(d_i{)}_{i=1,...,n}$ of $\ddot{I}†$-derivations satisfying appropriate conditions. Tuples of maps can be replaced by tuples of suitable elements $(c,u_1,...,u_n)$, whenever $A$ is a semisimple Clifford algebra.

30 pages