Seminário de Álgebra - "Specht property for the graded Jordan algebra of upper triangular matrices of order 2"

Nome: 
Manuela da Silva Souza (UFBA)
Data do Evento: 
quinta-feira, 16 de Agosto de 2018 - 14:00
Local do evento
Sala 323
Descrição: 

Let A be an algebra with non-trivial polynomial identity (or simply PI-algebra) and denote by Id(A) the T-ideal of all its polynomial identities. In general the description of a T-ideal is a hard problem. The ideal Id(A) of an algebra A satisfies the Specht property if Id(A) itself and all T-ideals containing Id(A) are finitely generated as Tideals. Kemer proved that every associative algebra over a field of characteristic 0 satisfies the Specht property. For associative algebras graded by a finite group the result remains valid. Different from the associative case, for non-associative algebras there is no general result in this direction not even when the characteristic of the field is 0. In the case of graded Lie or Jordan algebras we have experimental results, such that in [3] in which the authors proved the Specht property of IdG(sl2), the TG-ideal of the G-graded Lie algebra of 2×2 traceless matrices graded by any group G (non trivial), or in [5] in which a similar result was achieved for Bn, the finite dimensional Jordan algebra of a non-degenerate symmetric bilinear form graded by Z2. In this talk we use the finite basis property for sets to show the Specht property for the graded Jordan algebra of upper triangular matrices of order 2. This is joint work with L. Centrone and F. Martino ([1]).