15 research outputs found
Groebner bases of ideals invariant under endomorphisms
We introduce the notion of Groebner S-basis of an ideal of the free
associative algebra K over a field K invariant under the action of a
semigroup S of endomorphisms of the algebra. We calculate the Groebner S-bases
of the ideal corresponding to the universal enveloping algebra of the free
nilpotent of class 2 Lie algebra and of the T-ideal generated by the polynomial
identity [x,y,z]=0, with respect to suitable semigroups S. In the latter case,
if |X|>2, the ordinary Groebner basis is infinite and our Groebner S-basis is
finite. We obtain also explicit minimal Groebner bases of these ideals.Comment: 15 page