0000000000180827
AUTHOR
Lucio Centrone
A note on cocharacter sequence of Jordan upper triangular matrix algebra
Let UJn(F) be the Jordan algebra of n × n upper triangular matrices over a field F of characteristic zero. This paper is devoted to the study of polynomial identities satisfied by UJ2(F) and UJ3(F). In particular, the goal is twofold. On one hand, we complete the description of G-graded polynomial identities of UJ2(F), where G is a finite abelian group. On the other hand, we compute the Gelfand–Kirillov dimension of the relatively free algebra of UJ2(F) and we give a bound for the Gelfand–Kirillov dimension of the relatively free algebra of UJ3(F).
Specht property for some varieties of Jordan algebras of almost polynomial growth
Abstract Let F be a field of characteristic zero. In [25] it was proved that U J 2 , the Jordan algebra of 2 × 2 upper triangular matrices, can be endowed up to isomorphism with either the trivial grading or three distinct non-trivial Z 2 -gradings or by a Z 2 × Z 2 -grading. In this paper we prove that the variety of Jordan algebras generated by U J 2 endowed with any G-grading has the Specht property, i.e., every T G -ideal containing the graded identities of U J 2 is finitely based. Moreover, we prove an analogue result about the ordinary identities of A 1 , a suitable infinitely generated metabelian Jordan algebra defined in [27] .
Y-proper graded cocharacters of upper triangular matrices of order m graded by the m-tuple ϕ=(0,0,1,…,m−2)
Abstract Let F be a field of characteristic 0. We consider the algebra UT m ( F ) of upper triangular matrices of order m endowed with an elementary Z m -grading induced by the m-tuple ϕ = ( 0 , 0 , 1 , … , m − 2 ) , then we compute its Y-proper graded cocharacter sequence and we give the explicit formulas for the multiplicities in the case m = 2 , 3 , 4 , 5 .
Y-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4
Abstract Let F be a field of characteristic 0. We consider the upper triangular matrices with entries in F of size 2, 3 and 4 endowed with the grading induced by that of Vasilovsky. In this paper we give explicit computation for the multiplicities of the Y -proper graded cocharacters and codimensions of these algebras.