Invariant theory and reversible-equivariant vector fields

• Type: Article in International Scientific Journal
• Date: 2009

Authors

antoneli, f (Author) Other; baptistelli, ph (Author) Other; dias, aps (Author) FCUP; manoel, m (Author) Other

Journal

Title: Journal of Pure and Applied Algebra

Vol. 213 No. 4

Pages: 649-663

ISSN: 0022-4049

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 15 Citations

Scopus - 15 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-003-KGK

DOI: 10.1016/j.jpaa.2008.08.002

Abstract (EN): In this paper we present results for the systematic study of reversible-equivariant vector fields - namely, in the simultaneous presence of symmetries and reversing symmetries - by employing algebraic techniques from invariant theory for compact Lie groups. The Hilbert-Poincare series and their associated Molien formulae are introduced,and we prove the character formulae for the computation of dimensions of spaces of homogeneous anti-invariant polynomial functions and reversible-equivariant polynomial mappings. A symbolic algorithm is obtained for the computation of generators for the module of reversible-equivariant polynomial mappings over the ring of invariant polynomials. We show that this computation can be obtained directly from a well-known situation, namely from the generators of the ring of invariants and the module of the equivariants.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15