Gröbner bases for quadratic algebras of skew type

Ferran Cedó, Jan Okniński

Research output: Contribution to journalArticleResearchpeer-review

8 Citations (Scopus)

Abstract

Non-degenerate monoids of skew type are considered. This is a class of monoids S defined by n generators and n2 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 x N 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. © 2012 Edinburgh Mathematical Society.
Original languageEnglish
Pages (from-to)387-401
JournalProceedings of the Edinburgh Mathematical Society
Volume55
DOIs
Publication statusPublished - 1 Jun 2012

Keywords

  • finitely presented semigroup
  • normal form
  • regular language
  • semigroup
  • semigroup ring

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