Combinatorial Aspects of Capelli Identities and Structure of Algebras

Abstract

The combinatorial properties of the system of Capelli identities are investigated. These properties have enabled the author to develop a characteristic-free approach to the stucture theory of algebras satisfying Capelli identities with an arbitrary set of multilinear operations. The structure theory of those algebras is analogous to that of PI-algebras and finite-dimensional algebras. The obtained combinatorial properties also clarify the proof of the Braun — Kemer — Razmyslov theorem on the radical problem of an associative PI-algebra.