Model algebras, multiplicities, and representability indices of varieties of associative algebras

For a number of non-matrix varieties of associative algebras finite-dimensional (so-called model) algebras generating these varieties are calculated in this paper. In essence, the multiplicity and representability indices of such varieties are estimated. Simultaneously, an estimate of the multiplicity for a certain class of varieties of arbitrary complexity is given, which continues the previous studies of the author. The connection with quasipolynomials is also considered.