Title | **Gr\"obner bases for quadratic algebras of skew type.** |

Author(s) | Ferran Cedo, Jan Okninski |

Type | Article in Journal |

Abstract | Non-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 |

ISSN | 0013-0915; 1464-3839/e |

URL |
http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=8544918&fileId=S0013091511000447 |

Language | English |

Journal | Proc. Edinb. Math. Soc., II. Ser. |

Volume | 55 |

Number | 2 |

Pages | 387--401 |

Publisher | Cambridge University Press, Cambridge; Edinburgh Mathematical Society, Edinburgh |

Year | 2012 |

Edition | 0 |

Translation |
No |

Refereed |
No |