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X-Inner Automorphisms of Semi-Commutative Quantum Algebras

✍ Scribed by Jeffrey Bergen; Mark C Wilson

Publisher: Elsevier Science
Year: 1999
Tongue: English
Weight: 156 KB
Volume: 220
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1999.7927

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✦ Synopsis

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 * t G.

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