\(Y\)-proper graded cocharacters and codimensions of upper triangular matrices of size 2, 3, 4.
The authors consider graded polynomial identities of algebras over a field of characteristic 0. The algebras of upper triangular matrices play an important role in PI theory, and they are object of an extensive study. The graded identities of these algebras are of interest due to the extremal properties of the polynomial identities of upper triangular matrices. The main results in the paper under review consist in describing the graded codimensions and cocharacters for the upper triangular matrices of order up to 4. The authors give explicit formulae for the graded \(Y\)-proper codimensions and cocharacters (and their multiplicities). Here \(Y\) stands for the variables in the free graded associative algebra that are of degree 1 in the grading (the group being multiplicative).
scientific article; zbMATH DE number 6156191
scientific article