| Full text | |
| Author(s): |
Antoneli, Fernando
[1, 2, 3]
;
Baptistelli, Patricia H.
[4]
;
Dias, Ana Paula S.
[1, 2]
;
Manoel, Miriam
[5]
Total Authors: 4
|
| Affiliation: | [1] CMUP, P-4169007 Oporto - Portugal
[2] Univ Porto, Fac Ciencias, Dept Matemat Pura, P-4169007 Oporto - Portugal
[3] Univ Sao Paulo, Dept Matemat Aplicada, Inst Matemat & Estat, BR-05315970 Sao Paulo - Brazil
[4] Univ Estadual Maringa, Dept Matemat, Ctr Ciencias Exatas, BR-87020900 Maringa, Parana - Brazil
[5] Univ Sao Paulo, Dept Matemat, Inst Ciencias Matemat & Computacao, BR-31560970 Sao Carlos, SP - Brazil
Total Affiliations: 5
|
| Document type: | Journal article |
| Source: | Journal of Pure and Applied Algebra; v. 213, n. 5, p. 649-663, MAY 2009. |
| Web of Science Citations: | 11 |
| Abstract | |
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. (C) 2008 Elsevier B.V, All rights reserved. (AU) | |