IDENTITIES OF UNITARY FINITE-DIMENSIONAL ALGEBRAS

We deal with growth functions of sequences of codimensions of identities in finite-dimensional algebras with unity over a field of characteristic zero. For three-dimensional algebras, it is proved that the codimension sequence grows asymptotically as a(n), where a is 1, 2, or 3. For arbitrary finite-dimensional algebras, it is shown that the codimension growth either is polynomial or is not slower than 2(n). We give an example of a finite-dimensional algebra with growth rate a(n) with fractional exponent a = 3/3 root 4 + 1.