We study associative algebras with unity of polynomial codimension growth. For any fixed degree $k$ we construct associative algebras whose codimension sequence has the largest and the smallest possible polynomial growth of degree $k$. We also explicitly describe the identities and the exponential generating functions of these algebras.
GIAMBRUNO, A., LA MATTINA, D., PETROGRADSKY, V. (2007). Matrix algebras of polynomial codimension growth. ISRAEL JOURNAL OF MATHEMATICS, 158(158), 367-378 [10.1007/s11856-007-0017-7].
Matrix algebras of polynomial codimension growth
GIAMBRUNO, Antonino;LA MATTINA, Daniela;
2007-01-01
Abstract
We study associative algebras with unity of polynomial codimension growth. For any fixed degree $k$ we construct associative algebras whose codimension sequence has the largest and the smallest possible polynomial growth of degree $k$. We also explicitly describe the identities and the exponential generating functions of these algebras.
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