Multiplicities in the trace cocharacter sequence of two $4\times 4$ matrices

Multiplicities in the mixed trace cocharacter sequence of two $3\times 3$ matrices

We find explicitly the multiplicities in the (mixed) trace cocharacter sequence of two $3\times 3$ matrices over a field of characteristic 0 and show that asymptotically they behave as polynomials of seventh degree. As a consequence we obtain also the multiplicities of certain irreducible characters in the cocharacter sequence of the polynomial identities of $3\times 3$ matrices.

Cocharacters of polynomial identities of upper triangular matrices

We give an easy algorithm which calculates the generating function of the cocharacter sequence of the T-ideal of the polynomial identities of the algebra of upper triangular matrices over a field of characteristic zero. Applying this algorithm we have found the explicit form of the multiplicities in two cases: (i) for the "largest" partitions; (ii) for matrices of small size and for all partitions.

Cocharacters of polynomial identities of block triangular matrices

We give an algorithm which calculates the generating function of the cocharacter sequence of the polynomial identities of the algebra of upper block triangular (p+2q) x (p+2q) matrices over a field of characteristic zero with diagonal consisting of p copies of 1 x 1 and q copies of 2 x 2 matrices. We have found the explicit form of the multiplicities and their asymptotic behaviour for small values of p and q.

关于具有多项式恒等式的代数中心共特征的乘积数

On the multiplicities of the central cocharacter of algebras with polynomial identities

本文研究了具有多项式恒等式的代数的共特征序列，通过分析PI-代数的例子，实现了对列长和中心列长序列受限代数的完整分类。

Y-proper graded cocharacters of upper-triangular matrices od order m graded by the m-tuple ϕ=(0,0,1,...,m-2)

Let F be a field of characteristic 0. We consider the algebra UT_m(F) of upper triangular matrices of order m endowed with na elementar Z_m-grading induced by the m-tuple phi=(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.

关于某些PI代数的共特征序列

On the cocharacter sequence of some PI-algebras

本文研究了某些PI代数的共特征序列，证明了具有单位元的代数的共特征宽度与李-nilpotency性质等价，并探讨了其在非交换不变量理论中的应用。