Automorphic equivalence of the representations of Lie algebras

Autor(es)

Shestakov, I. ; Tsurkov, A.

• Tipo de documento: Artigo Científico
• Fonte: ALGEBRA & DISCRETE MATHEMATICS; v. 15, n. 1, p. 31-pg., 2013-01-01.

Resumo

In this paper we research the algebraic geometry of the representations of Lie algebras over fixed field k. We assume that this field is infinite and char (k) = 0. We consider the representations of Lie algebras as 2-sorted universal algebras. The representations of groups were considered by similar approach: as 2-sorted universal algebras - in [3] and [2]. The basic notions of the algebraic geometry of representations of Lie algebras we define similar to the basic notions of the algebraic geometry of representations of groups (see [2]). We prove that if a field k has not nontrivial automorphisms then automorphic equivalence of representations of Lie algebras coincide with geometric equivalence. This result is similar to the result of [4], which was achieved for representations of groups. But we achieve our result by another method: by consideration of 1-sorted objects. We suppose that our method can be more perspective in the further researches. (AU)

• Processo FAPESP: 10/50948-2 - Universal algebraic geometry.
• Beneficiário: Arkady Tsurkov
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 10/50347-9 - Álgebras, representações e aplicações
• Beneficiário: Ivan Chestakov
• Modalidade de apoio: Auxílio à Pesquisa - Temático