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Reversible skew laurent polynomial rings and deformations of poisson automorphisms

Jordan, D.A. and Sasom, N. (2009) Reversible skew laurent polynomial rings and deformations of poisson automorphisms. Journal of Algebra and Its Applications, 8 (5). pp. 733-757. ISSN 0219-4988

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Abstract

A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1). We study invariants for reversing automorphisms and apply our methods to determine the rings of invariants of reversing automorphisms of the two most familiar examples of simple skew Laurent polynomial rings, namely a localization of the enveloping algebra of the two-dimensional non-abelian solvable Lie algebra and the coordinate ring of the quantum torus, both of which are deformations of Poisson algebras over the base field F. Their reversing automorphisms are deformations of Poisson automorphisms of those Poisson algebras. In each case, the ring of invariants of the Poisson automorphism is the coordinate ring B of a surface in F-3 and the ring of invariants S-theta of the reversing automorphism is a deformation of B and is a factor of a deformation of F[x(1), x(2), x(3)] for a Poisson bracket determined by the appropriate surface.

Item Type: Article
Copyright, Publisher and Additional Information: © 2009 World Scientific. This is an author produced version of a paper subsequently published in Journal of Algebra and its Applications. Uploaded in accordance with the publisher's self-archiving policy
Keywords: Skew Laurent polynomial ring; Poisson automorphism; invariants
Institution: The University of Sheffield
Academic Units: The University of Sheffield > Faculty of Science (Sheffield) > School of Mathematics and Statistics (Sheffield)
Depositing User: Miss Anthea Tucker
Date Deposited: 02 Dec 2009 17:03
Last Modified: 08 Feb 2013 16:59
Published Version: http://dx.doi.org/10.1142/S0219498809003564
Status: Published
Publisher: World Scientific Publishing
Refereed: Yes
Identification Number: 10.1142/S0219498809003564
URI: http://eprints.whiterose.ac.uk/id/eprint/10226

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