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Partial mirror symmetry, lattice presentations and algebraic monoids

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Publication details

JournalProceedings of the London Mathematical Society
DateE-pub ahead of print - 5 Feb 2013
DatePublished (current) - 2 Aug 2013
Issue number2
Number of pages37
Pages (from-to)414-450
Early online date5/02/13
Original languageEnglish


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.

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(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.

    Research areas

  • Algebra

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