Reciprocal polynomials and modular invariant theory

Woodcock, Chris F. (2007) Reciprocal polynomials and modular invariant theory. Transformation Groups, 12 (4). pp. 787-806. ISSN 1083-4362 . (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided)

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Let p be a prime and let V be a finite-dimensional vector space over the field F-p. In this paper we introduce, and study some basic properties of, the algebra of reciprocal polynomials A(V). This can be regarded as a purely inseparable integral extension of the symmetric algebra S(V*) of the dual space V* and has a closely related modular invariant theory with a provable degree bound for invariants which is only conjectural in the symmetric algebra case. The graded F-p- algebra A(V) turns out to be normal and Cohen-Macaulay, there is an analogue of Steenrod powers and also a "Karagueuzian and Symonds-type" finiteness theorem for its invariant theory, etc.

Item Type: Article
Subjects: Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science > Pure Mathematics
Depositing User: Suzanne Duffy
Date Deposited: 25 Apr 2008 08:29
Last Modified: 23 May 2014 08:50
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