A note on affine representable algebras

Abstract

We consider affine representable algebras, that is, finitely generated algebras over a field that can be embedded into some matrix algebra over a commutative algebra. We show that this algebra can in fact be chosen to be a polynomial algebra. We also prove a refined version of a theorem of V.T. Markov stating that the Gelfand-Kirillov dimension of any affine representable algebra is an integer.

minor edits and corrections; question added at end of article