Looking for Gröbner basis theory for (almost) skew 2-nomial algebras

• Autores: Huishi Li
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 45, Nº 9, 2010, págs. 918-942
• Idioma: inglés
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• Resumen

  • In this paper, we introduce (almost) skew 2-nomial algebras and look for a one-sided or two-sided Gröbner basis theory for such algebras at a modest level. That is, we establish the existence of a skew multiplicative K-basis for every skew 2-nomial algebra, and we explore the existence of a (left, right, or two-sided) monomial ordering for an (almost) skew 2-nomial algebra. As distinct from commonly recognized algebras holding a Gröbner basis theory (such as algebras of the solvable type (Kandri-Rody and Weispfenning, 1990) and some of their homomorphic images), a subclass of skew 2-nomial algebras that have a left Gröbner basis theory but may not necessarily have a two-sided Gröbner basis theory, respectively a subclass of skew 2-nomial algebras that have a right Gröbner basis theory but may not necessarily have a two-sided Gröbner basis theory, are determined such that numerous quantum binomial algebras (which provide binomial solutions to the Yang�Baxter equation) and their Koszul dual ([Gateva-Ivanova and Van den Bergh, 1998], [Laffaille, 2000] and [Gateva-Ivanova, 2009]) are involved.