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TitleGr\"obner bases for quadratic algebras of skew type.
Author(s) Ferran Cedo, Jan Okninski
TypeArticle in Journal
AbstractNon-degenerate monoids of skew type are considered. This is a class of monoids S defined by n generators and $\binom{n}{2}$ quadratic relations of certain type, which includes the class of monoids yielding set-theoretic solutions of the quantum Yang–Baxter equation, also called binomial monoids (or monoids of I-type with square-free defining relations). It is shown that under any degree-lexicographic order on the associated free monoid FMn. of rank n the set of normal forms of elements of S is a regular language in FMn. As one of the key ingredients of the proof, it is shown that an identity of the form xN yN = yN xN holds in S. The latter is derived via an investigation of the structure of S viewed as a semigroup of matrices over a field. It also follows that the semigroup algebra K[S] is a finite module over a finitely generated commutative subalgebra of the form K[A] for a submonoid A of S.
Keywords finitely presented semigroup; semigroup ring; semigroup; normal form; regular language
ISSN0013-0915; 1464-3839/e
URL http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8544918&fileId=S0013091511000447
JournalProc. Edinb. Math. Soc., II. Ser.
PublisherCambridge University Press, Cambridge; Edinburgh Mathematical Society, Edinburgh
Translation No
Refereed No