Jeffrey Bergen and Mark C. Wilson, Journal of Algebra 220, (1999), 152-173.
Abstract: Many important quantum algebras such as quantum symplectic space, quantum euclidean space, quantum matrices, $latex q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $latex U(L_+)$ of even Lie color algebras are also semi-commutative. In this paper, we generalize work of Montgomery and examine the X-inner automorphisms of such algebras.
The theorems and examples in our paper show that for algebras $latex R$ of this type, the non-identity X-inner automorphisms of $latex R$ tend to have infinite order. Thus if $latex G$ is a finite group of automorphisms of $latex R$, then the action of $latex G$ will be X-outer and this immediately gives useful information about crossed products $latex R*_t G$.