Weak G-identities for the Pair (M2(C),sl2(C))

Autor(es)

Codamo, Ramon ; Koshlukov, Plamen

• Tipo de documento: Artigo Científico
• Fonte: ALGEBRAS AND REPRESENTATION THEORY; v. N/A, p. 17-pg., 2025-01-02.

Resumo

In this paper we study algebras acted on by a finite group G and the corresponding Gidentities. Let M2(C) be the 2 x 2 matrix algebra over the field of complex numbers C and let sl2(C) be the Lie algebra of traceless matrices in M2(C). Assume that G is a finite group acting as a group of automorphisms on M2(C). These groups were described in the Nineteenth century, they consist of the finite subgroups of PGL2(C), which are, up to conjugacy, the cyclic groups Zn, the dihedral groups Dn (of order 2n), the alternating groups A4 and A5, and the symmetric group S4. The G-identities for M2(C) were described by Berele. The finite groups acting on sl2(C) are the same as those acting on M2(C). The G-identities for the Lie algebra of the traceless sl2(C) were obtained by Mortari and by the second author. We study the weak G-identities of the pair (M2(C), sl2(C)), when G is a finite group. Since every automorphism of the pair is an automorphism for M2(C), it follows from this that G is one of the groups above. In this paper we obtain bases of the weak G-identities for the pair (M2(C), sl2(C)) when G is a finite group acting as a group of automorphisms. (AU)

• Processo FAPESP: 18/23690-6 - Estruturas, representações e aplicações de sistemas algébricos
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático