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John Fountain

Publications and source records attributed to John Fountain.

4 recordsLinked to original sources
arXiv2011

Partial mirror symmetry, lattice presentations and algebraic monoids

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 arXiv:0812.2789. 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.

math.GR↗
arXiv2008

Partial symmetry, reflection monoids and Coxeter groups

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.

math.GR↗
arXiv2008

Graph products of right cancellative monoids

Our first main result shows that a graph product of right cancellative monoids is itself right cancellative. If each of the component monoids satisfies the condition that the intersection of two principal left ideals is either principal or empty, then so does the graph product. Our second main result gives a presentation for the inverse hull of such a graph product. We then specialise to the case of the inverse hulls of graph monoids, obtaining what we call polygraph monoids. Among other properties, we observe that polygraph monoids are F*-inverse. This follows from a general characterisation of those right cancellative monoids with inverse hulls that are F*-inverse.

math.RA↗
arXiv2007

Partial mirror symmetry I: reflection monoids

This is the first of a series of papers in which we initiate and develop the theory of reflection monoids, motivated by the theory of reflection groups. The main results identify a number of important inverse semigroups as reflection monoids, introduce new examples, and determine their orders.

math.GR↗