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pro vyhledávání: '"Lawson, Mark A."'
Autor:
Lawson, Mark V.
In this paper, we describe \'etale Boolean right restriction monoids in terms of Boolean inverse monoids.
Externí odkaz:
http://arxiv.org/abs/2404.08606
Autor:
Lawson, Mark V.
This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.
Comment: arXiv admin note: text overlap with arXiv:2006.01628
Comment: arXiv admin note: text overlap with arXiv:2006.01628
Externí odkaz:
http://arxiv.org/abs/2304.13580
Autor:
Lawson, Mark V.
We prove that there is an adjunction between what we call \'etale topological categories and restriction quantal frames that leads to an adjunction with a category of complete restriction monoids. This generalizes the adjunction between \'etale group
Externí odkaz:
http://arxiv.org/abs/2303.05188
Autor:
Lawson, Mark V.
We show explicitly that Boolean inverse semigroups are in duality with what we term Boolean groupoids. This generalizes the classical Stone duality, which we refer to as commutative Stone duality, between generalized Boolean algebras and locally comp
Externí odkaz:
http://arxiv.org/abs/2207.02686
Autor:
Lawson, Mark V., Scott, Philip
A countably infinite Boolean inverse monoid that can be written as an increasing union of finite Boolean inverse monoids (suitably embedded) is said to be of finite type. Borrowing terminology from $C^{\ast}$-algebra theory, we say that such a Boolea
Externí odkaz:
http://arxiv.org/abs/2204.10033
Publikováno v:
In Journal of Pure and Applied Algebra January 2024 228(1)
Autor:
Lawson, Mark V.
We describe the structure of finite Boolean inverse monoids and apply our results to the representation theory of finite inverse semigroups. We then generalize to semisimple Boolean inverse semigroups.
Externí odkaz:
http://arxiv.org/abs/2102.12931
Autor:
Lawson, Mark V
We formulate an alternative approach to describing Ehresmann semigroups by means of left and right \'etale actions of a meet semilattice on a category. We also characterize the Ehresmann semigroups that arise as the set of all subsets of a finite cat
Externí odkaz:
http://arxiv.org/abs/2102.12250
We construct a family of groups from suitable higher rank graphs which are analogues of the finite symmetric groups. We introduce homological invariants showing that many of our groups are, for example, not isomorphic to $nV$, when $n \geq 2$.
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Externí odkaz:
http://arxiv.org/abs/2010.08960
Autor:
Lawson, Mark V
We revisit our construction of the Thompson groups from the polycyclic inverse monoids in the light of new research. Specifically, we prove that the Thompson group $G_{n,1}$ is the group of units of a Boolean inverse monoid $C_{n}$ called the Cuntz i
Externí odkaz:
http://arxiv.org/abs/2006.15338