On closed Lie ideals of certain tensor products of C*-algebras II

Abstract

We identify all closed Lie ideals of $A{\otimes }^{\alpha }B$ and $B(H){\otimes }^{\alpha }B(H)$, where ${\otimes }^{\alpha }$ is either the Haagerup tensor product, the Banach space projective tensor product or the operator space projective tensor product, $A$ is any simple C*-algebra, $B$ is any C*-algebra with one of them admitting no tracial states, and $H$ is an infinite dimensional separable Hilbert space. Further, generalizing a result of Marcoux, we also identify all closed Lie ideals of $A{\otimes }^{\min }B$, where $A$ is a simple C*-algebra with at most one tracial state and $B$ is any commutative C*-algebra.

A small error in proof of Proposition 4.1 has been fixed