41 research outputs found
Nil algebras, Lie algebras and wreath products with intermediate and oscillating growth
We construct finitely generated nil algebras with prescribed growth rate. In
particular, any increasing submultiplicative function is realized as the growth
function of a nil algebra up to a polynomial error term and an arbitrarily slow
distortion. We then move on to examples of nil algebras and domains with
strongly oscillating growth functions and construct primitive algebras for
which the Gelfand-Kirillov dimension is strictly sub-additive with respect to
tensor products, thus answering a question raised by Krempa-Okninski and
Krause-Lenagan
Automorphisms and derivations of affine commutative and PI-algebras
We prove analogs of A.~Selberg's result for finitely generated subgroups of
and of Engel's theorem for subalgebras of for a
finitely generated associative commutative algebra over an associative
commutative ring. We prove also an analog of the theorem of W.~Burnside and
I.~Schur about locally finiteness of torsion subgroups of