We introduce the notion of Gröbner S-basis of an ideal of the free associative algebra K<X> over a field K invariant under the action of a semigroup S of endomorphisms of the algebra. We calculate the Gröbner 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 Gröbner basis is infinite and our Gröbner S-basis is finite. We obtain also explicit minimal Gröbner bases of these ideals.

Grobner bases of ideals invariant under endomorphisms

LA SCALA, Roberto
2006

Abstract

We introduce the notion of Gröbner 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 Gröbner 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 Gröbner basis is infinite and our Gröbner S-basis is finite. We obtain also explicit minimal Gröbner bases of these ideals.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11586/13368
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