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CONFORMAL $\mathcal{s}$$\mathcal{l}$2 ENVELOPING ALGEBRAS AS AMBISKEW POLYNOMIAL RINGS

Published online by Cambridge University Press:  05 February 2002

Martin O’Neill
Martin O’Neill
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW, UK ([email protected])
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Abstract

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We study a three parameter deformation $\mathcal{U}_{abc}$ of $\mathcal{U}(\mathfrak{sl}_2)$ introduced by Le Bruyn in 1995. Working over an arbitrary algebraically closed field of characteristic zero, we determine the centres, the finite-dimensional irreducible representations, and, when the parameter $a$ is not a non-trivial root of unity, the prime ideals of those $\mathcal{U}_{abc}$, with $ac\neq0$, which are conformal as ambiskew polynomial rings.

AMS 2000 Mathematics subject classification: Primary 16W35; 17B37. Secondary 16S36; 16S80

Keywords

quantum $\mathfrak{sl}_2$ enveloping algebrasiterated skew polynomial ringsprime ideals
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 45 , Issue 1 , February 2002 , pp. 91 - 115
Copyright
Copyright © Edinburgh Mathematical Society 2002