Computing with 2\(\times 2\) matrices (Q792420)

The author studies important objects in PI-theory - the algebra of matrices and their traces, the subalgebra of generic matrices and the centres of these algebras. For 2\(\times 2\) matrices over an infinite field of characteristic \(\neq 2,3\) he describes these objects in a precise way. He finds linear bases and computes their Poincaré (or Hilbert) series as graded vector spaces. The proofs are based on the technique of Young diagrams and invariant theory. Recently, a part of these results have been obtained in characteristic 0 by the reviewer [C. R. Acad. Bulg. Sci. 34, 1201-1204 (1981; Zbl 0496.16018)] independently and from a different point of view. Using other ideas, \textit{E. Formanek} [J. Algebra 89, 178-223 (1984)] has generalized some of them.