Gröbner bases and syzygies on bimodules over PBW algebras

• Autores: Manuel García Román, Socorro García Román
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 40, Nº 3, 2005, págs. 1039-1052
• Idioma: inglés
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• Resumen

  • A new method for the computation of two-sided Gröbner bases of ideals and bimodules shifting the problem to the enveloping algebra is proposed. This alternative method appears to be more efficient than the one in [Kandri-Rody, A., Weispfenning, V., 1990. Non-commutative Gröbner bases in algebras of solvable type. J. Symbolic Comput. 9, 1¿26] since it calls the left Buchberger algorithm once. We introduce the notion, arising from the ideas that this method involves, of two-sided syzygy, which is revealed to be useful in the computation of, e.g., the intersection of bimodules. Further applications are left for a later work.