On the freeness problem for truncated current algebras

Autor(es)

Benitez, German ; Rocha, Henrique

• Tipo de documento: Artigo Científico
• Fonte: SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES; v. 15, n. 1, p. 18-pg., 2021-01-20.

Resumo

Molev (in: Doebner, Scherer, Nattermann (eds) Group 21, physical applications and mathematical aspects of geometry, groups, and algebras, World Scientific, Singapore, vol 1, pp 172-176, 1997) constructed generators of the center of the universal enveloping algebra U(g(m)(n)) for the truncated current Lie algebra g(m)(n) = gl(n)circle times C[x]/(x(m)). Such generators allow to define algebraic varieties associated to the center and the Gelfand-Tsetlin subalgebra. In this paper we prove that the Gelfand-Tsetlin variety is equidimensional of dimension mn(n - 1)/2 if and only if n = 1, 2, implying that U(g(m)(2)) is free over the Gelfand-Tsetlin subalgebra. (AU)

• Processo FAPESP: 18/12382-9 - Representações de álgebras correntes
• Beneficiário: Henrique de Oliveira Rocha
• Modalidade de apoio: Bolsas no Brasil - Mestrado