The Experts below are selected from a list of 36129 Experts worldwide ranked by ideXlab platform
Mark V Lawson - One of the best experts on this subject based on the ideXlab platform.
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graph inverse Semigroups their characterization and completion
2014Co-Authors: David G Jones, Mark V LawsonAbstract:Abstract Graph inverse Semigroups generalize the polycyclic inverse monoids and play an important role in the theory of C ⁎ -algebras. In this paper, we characterize such Semigroups and show how they may be completed, under suitable conditions, to form what we call the Cuntz–Krieger semigroup of the graph. This semigroup is proved to be the ample semigroup of a topological groupoid associated with the graph, and the semigroup analogue of the Leavitt path algebra of the graph.
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non commutative stone duality inverse Semigroups topological groupoids and c algebras
2012Co-Authors: Mark V LawsonAbstract:We study a non-commutative generalization of Stone duality that connects a class of inverse Semigroups, called Boolean inverse ∧-Semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper is given over to showing that Boolean inverse ∧-Semigroups arise as completions of inverse ∧-Semigroups we call pre-Boolean. An inverse ∧-semigroup is pre-Boolean if and only if every tight filter is an ultrafilter, where tight filters are defined by combining ideas of both Exel and Lenz. A simple necessary condition for a semigroup to be pre-Boolean is derived and a variety of examples of inverse Semigroups are shown to satisfy it. Thus the polycyclic inverse monoids, and certain Rees matrix Semigroups over the polycyclics, are pre-Boolean and it is proved that the groups of units of their completions are precisely the Thompson–Higman groups Gn, r. The inverse Semigroups arising from suitable directed graphs are also pre-Boolean and the topological groupoids arising from these graph inverse Semigroups under our non-commutative Stone duality are the groupoids that arise from the Cuntz–Krieger C*-algebras. An elementary application of our theory shows that the finite, fundamental Boolean inverse ∧-Semigroups are just the finite direct products of finite symmetric inverse monoids. Finally, we explain how tight filters are related to prime filters setting the scene for future work.
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non commutative stone duality inverse Semigroups topological groupoids and c algebras
2011Co-Authors: Mark V LawsonAbstract:We study a non-commutative generalization of Stone duality that connects a class of inverse Semigroups, called Boolean inverse $\wedge$-Semigroups, with a class of topological groupoids, called Hausdorff Boolean groupoids. Much of the paper is given over to showing that Boolean inverse $\wedge$-Semigroups arise as completions of inverse Semigroups we call pre-Boolean. An inverse $\wedge$-semigroup is pre-Boolean if and only if every tight filter is an ultrafilter, where the definition of a tight filter is obtained by combining work of both Exel and Lenz. A simple necessary condition for a semigroup to be pre-Boolean is derived and a variety of examples of inverse Semigroups are shown to satisfy it. Thus the polycyclic inverse monoids, and certain Rees matrix Semigroups over the polycyclics, are pre-Boolean and it is proved that the groups of units of their completions are precisely the Thompson-Higman groups $G_{n,r}$. The inverse Semigroups arising from suitable directed graphs are also pre-Boolean and the topological groupoids arising from these graph inverse Semigroups under our non-commutative Stone duality are the groupoids that arise from the Cuntz-Krieger $C^{\ast}$-algebras.
Charles Starling - One of the best experts on this subject based on the ideXlab platform.
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boundary quotients of c algebras of right lcm Semigroups
2015Co-Authors: Charles StarlingAbstract:Abstract We study C*-algebras associated to right LCM Semigroups, that is, Semigroups which are left cancellative and for which any two principal right ideals are either disjoint or intersect in another principal right ideal. If P is such a semigroup, its C*-algebra admits a natural boundary quotient Q ( P ) . We show that Q ( P ) is isomorphic to the tight C*-algebra of a certain inverse semigroup associated to P, and thus is isomorphic to the C*-algebra of an etale groupoid. We use this to give conditions on P which guarantee that Q ( P ) is simple and purely infinite, and give applications to self-similar groups and Zappa–Szep products of Semigroups.
Karen D Aucoin - One of the best experts on this subject based on the ideXlab platform.
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the structure of commutative Semigroupswith the ideal retraction property
2004Co-Authors: Karen D Aucoin, Jill A Dumesnil, J A HildebrantAbstract:A semigroup is said to have the ideal retraction property when each of its ideals is a homomorphic retraction of the whole semigroup. This paper presents a complete characterization of the commutative Semigroups that enjoy this property. The fundamental building blocks of these Semigroups are the 2-cores and the semilattice of idempotents. Structure for semilattices with the ideal retraction property was discussed in an earlier paper and the structure of the 2-core is described in detail within this paper.
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the structure of commutative Semigroups with the ideal extension property
2004Co-Authors: Karen D AucoinAbstract:A semigroup is said to have the ideal retraction property when each of its ideals is a homomorphic retraction of the whole semigroup. This paper presents a complete characterization of the commutative Semigroups that enjoy this property. The fundamental building blocks of these Semigroups are the 2-cores and the semilattice of idempotents. Structure for semilattices with the ideal retraction property was discussed in an earlier paper and the structure of the 2-core is described in detail within this paper.
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commutative periodic Semigroups with the ideal retraction property
2002Co-Authors: Karen D Aucoin, Jill A Dumesnil, J A HildebrantAbstract:This paper presents a complete characterization of commutative periodic Semigroups with the ideal retraction property. These Semigroups are those with the property that each ideal is a homomorphic retraction of the semigroup. As a consequence of this characterization it is established that the ideal retraction property is hereditary and preserved by homomorphisms for commutative periodic Semigroups.
A Vignerontenorio - One of the best experts on this subject based on the ideXlab platform.
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Semigroups with fixed multiplicity and embedding dimension
2019Co-Authors: J I Garciagarcia, J C Rosales, D Marinaragon, M A Morenofrias, A VignerontenorioAbstract:Given m ∈ ℕ , a numerical semigroup with multiplicity m is called a packed numerical semigroup if its minimal generating set is included in { m , m + 1, …, 2 m − 1} . In this work, packed numerical Semigroups are used to build the set of numerical Semigroups with a given multiplicity and embedding dimension, and to create a partition of this set. Wilf’s conjecture is verified in the tree associated to some packed numerical Semigroups. Furthermore, given two positive integers m and e , some algorithms for computing the minimal Frobenius number and minimal genus of the set of numerical Semigroups with multiplicity m and embedding dimension e are provided. We also compute the Semigroups where these minimal values are achieved.
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Semigroups with fixed multiplicity and embedding dimension
2017Co-Authors: J I Garciagarcia, J C Rosales, D Marinaragon, M A Morenofrias, A VignerontenorioAbstract:Given $m\in \mathbb{N},$ a numerical semigroup with multiplicity $m$ is called packed numerical semigroup if its minimal generating set is included in $\{m,m+1,\ldots, 2m-1\}.$ In this work, packed numerical Semigroups are used to built the set of numerical Semigroups with fixed multiplicity and embedding dimension, and to create a partition in this set. Moreover, Wilf's conjecture is checked in the tree associated to some packed numerical Semigroups.
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on convex polyhedron Semigroups
2015Co-Authors: J I Garciagarcia, A VignerontenorioAbstract:Let $\mathbf{F}$ be bounded convex polyhedron of $\R^3_{\geq}$ and $\psi_k$ the homothety with center the origin and radius $k$. The convex polyhedron semigroup associated to $\mathbf{F}$ is the semigroup $\cup_{k\in\N}\psi_k(\mathbf{F})\cap \N^3$. In this work, we use topological and discrete geometrical tools to study this class of Semigroups. We give conditions to know when one of these Semigroups is finitely generated, we characterize the Cohen-Macaulay and Buchsbaum properties, and we provide a family of Gorenstein affine Semigroups.
Volodymyr Mazorchuk - One of the best experts on this subject based on the ideXlab platform.
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combinatorial gelfand models for some Semigroups and q rook monoid algebras
2009Co-Authors: Ganna Kudryavtseva, Volodymyr MazorchukAbstract:Inspired by the results of Adin, Postnikov and Roichman, we propose combinatorial Gelfand models for semigroup algebras of some finite Semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup and the factor power of the symmetric group. Furthermore, we extend the Gelfand model for the semigroup algebras of the symmetric inverse semigroup to a Gelfand model for the q -rook monoid algebra.
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combinatorial gelfand models for some Semigroups and q rook monoid algebras
2007Co-Authors: Ganna Kudryavtseva, Volodymyr MazorchukAbstract:Inspired by the results of [R. Adin, A. Postnikov, Y. Roichman, Combinatorial Gelfand model, preprint math.RT arXiv:0709.3962], we propose combinatorial Gelfand models for semigroup algebras of some finite Semigroups, which include the symmetric inverse semigroup, the dual symmetric inverse semigroup, the maximal factorizable subsemigroup in the dual symmetric inverse semigroup, and the factor power of the symmetric group. Furthermore we extend the Gelfand model for the semigroup algebras of the symmetric inverse semigroup to a Gelfand model for the $q$-rook monoid algebra.
