# 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. (doi:10.1007/s00031-006-0043-2) (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) (KAR id:2819)

 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. Official URLhttp://dx.doi.org/10.1007/s00031-006-0043-2

## Abstract

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 10.1007/s00031-006-0043-2 Q Science > QA Mathematics (inc Computing science) Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science Suzanne Duffy 25 Apr 2008 08:29 UTC 16 Nov 2021 09:41 UTC https://kar.kent.ac.uk/id/eprint/2819 (The current URI for this page, for reference purposes) https://orcid.org/0000-0003-4713-0040