6533b831fe1ef96bd12990f0

RESEARCH PRODUCT

Graded polynomial identities and Specht property of the Lie algebrasl2

Antonino GiambrunoManuela Da Silva Souza

subject

Filtered algebraDiscrete mathematicsPure mathematicsAlgebra and Number TheoryLie algebraDifferential graded algebraGraded ringSpecht moduleCellular algebraLie superalgebraMathematicsLie conformal algebraGraded Lie algebra

description

Abstract Let G be a group. The Lie algebra sl 2 of 2 × 2 traceless matrices over a field K can be endowed up to isomorphism, with three distinct non-trivial G-gradings induced by the groups Z 2 , Z 2 × Z 2 and Z . It has been recently shown (Koshlukov, 2008 [8] ) that for each grading the ideal of G-graded identities has a finite basis. In this paper we prove that when char ( K ) = 0 , the algebra sl 2 endowed with each of the above three gradings has an ideal of graded identities Id G ( sl 2 ) satisfying the Specht property, i.e., every ideal of graded identities containing Id G ( sl 2 ) is finitely based.

yearjournalcountryeditionlanguage
2013-09-01Journal of Algebra
https://doi.org/10.1016/j.jalgebra.2013.05.009