Tensor sum of infinitesimal generators

Abstract

‎Let $A$ and $B$ be $C^*$-algebras‎, ‎and let $\delta$ be a derivation on the tensor product $A\otimes B$ endowed with a uniform cross norm‎. ‎In this paper‎, ‎we present a decomposition for $\delta$ as $\delta=\Delta \otimes id‎+ ‎id\otimes‎

‎\nabla$‎, ‎where $id$ stands for the identity operator and $\Delta$ and $\nabla$ are derivations on $A$ and $B$‎, ‎respectively‎. ‎We investigate the concept of flow on the tensor product of $C^*$-algebras and some properties of tensor sum are presented‎.