Some remarks on trace cocharacters
The cocharacter sequences are one of the important numerical characteristics of a PI algebra. There are many connections between the cocharacters and the trace cocharacters, and it is often desirable to pass from one to the other in order to avoid complicated calculations. The authors study the pure and the mixed trace cocharacters of algebras over a field of characteristic zero. First they show that the cocharacter sequences are Young derived if the algebra is unitary PI with nonzero trace. In addition the pure trace cocharacter sequence is not twice Young derived while the mixed one is not triple Young derived. Then the algebras \(M_{k,l}\) are considered. They are an important example for the above results. It turns out that when \(k\neq l\) the mixed trace cocharacters are Young derived, and when \(k=l\) they are not Young derived. Some other important applications (both structural and combinatorial) are made for the cocharacters of the algebra of all diagonal \(n\times n\) matrices as well as of the algebra of all upper triangular \(2\times 2\) matrices.
scientific article; zbMATH DE number 815880