X-inner automorphisms of semi-commutative quantum algebras

Details X-inner automorphisms of semi-commutative quantum algebras X-inner automorphisms of semi-commutative quantum algebras

1998-04-22

arxiv.org/abs/math/9804109v1

Mathematics

Rings and Algebras

20 pages, in AMS-TeX

Scientific paper

Many important quantum algebras such as quantum symplectic space, quantum Euclidean space, quantum matrices, $q$-analogs of the Heisenberg algebra and the quantum Weyl algebra are semi-commutative. In addition, enveloping algebras $U(L_+)$ 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 $R$ of this type, the non-identity $X$-inner automorphisms of $R$ tend to have infinite order. Thus if $G$ is a finite group of automorphisms of $R$, then the action of $G$ will be $X$-outer and this immediately gives useful information about crossed products $R*_tG$.

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