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Journal | Proceedings of the London Mathematical Society |
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Date | E-pub ahead of print - 5 Feb 2013 |

Date | Published (current) - 2 Aug 2013 |

Issue number | 2 |

Volume | 107 |

Number of pages | 37 |

Pages (from-to) | 414-450 |

Early online date | 5/02/13 |

Original language | English |

This is the second in a series of papers that develops the theory of reflection monoids, motivated by the theory of reflection groups. Reflection monoids were first introduced in Everitt and Fountain [Adv. Math. 223 (2010) 1782–1814]. In this paper, we study their presentations as abstract monoids. Along the way, we also find general presentations for certain join-semilattices (as monoids under join), which we interpret for two special classes of examples: the face lattices of convex polytopes and the geometric lattices, particularly the intersection lattices of hyperplane arrangements. Another spin-off is a general presentation for the Renner monoid of an algebraic monoid, which we illustrate in the special case of the ‘classical’ algebraic monoids.

(c) 2013 London Mathematical Society. his is an author produced version of a paper published in Proceedings of the London Mathematical Society. Uploaded in accordance with the publisher's self-archiving policy.

- Algebra

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