Abstract :
Finitely generated linear semigroups S subset of or equal to Mn(K) of polynomial growth are described. First, we introduce the class of almost unipotent semigroups and discuss their growth functions. Next, the structure of an arbitrary semigroup S subset of or equal to Mn(K) of polynomial growth is described in terms of certain almost unipotent semigroups derived from S. The description in the characteristic zero case is more complicated than in the positive characteristic, settled previously, because finitely generated almost unipotent semigroups must be finite in the latter case.
