Representation Theory of Semigroups
Lead Research Organisation:
Heriot-Watt University
Department Name: S of Mathematical and Computer Sciences
Abstract
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Organisations
People |
ORCID iD |
| Mark Verus Lawson (Principal Investigator) |
Publications
Jones D
(2014)
Graph inverse semigroups: Their characterization and completion
in Journal of Algebra
Kudryavtseva G
(2013)
The structure of generalized inverse semigroups
in Semigroup Forum
Kudryavtseva G
(2015)
Boolean sets, skew Boolean algebras and a non-commutative Stone duality
in Algebra universalis
Kudryavtseva G
(2015)
The classifying space of an inverse semigroup
in Periodica Mathematica Hungarica
Kudryavtseva G
(2017)
A perspective on non-commutative frame theory
in Advances in Mathematics
Kudryavtseva G
(2014)
A perspective on non-commutative frame theory
Kudryavtseva G
(2015)
Invariant means on Boolean inverse monoids
in Semigroup Forum
Lawson M
(2017)
Tarski monoids: Matui's spatial realization theorem
in Semigroup Forum
Lawson M
(2016)
Subgroups of the group of homeomorphisms of the Cantor space and a duality between a class of inverse monoids and a class of Hausdorff étale groupoids
in Journal of Algebra
Lawson M
(2017)
AF inverse monoids and the structure of countable MV-algebras
in Journal of Pure and Applied Algebra
| Description | Boolean algebras were introduced to model aspects of the way we reason. They have been applied in practical settings such as the design of computers and in theoretical settings such as the foundations of measure theory. Boolean inverse semigroups generalize Boolean algebras to a non-commutative framework: the `and' is replaced by the (non-commutative) multiplication and the `or' by a partial join operation. We have shown that these semigroups are tightly involved in the construction of interesting classes of infinite groups. |
| Exploitation Route | This work is clearly important for anyone interested in the theory of C*-algebras. |
| Sectors | Digital/Communication/Information Technologies (including Software),Electronics,Other |
| Description | Research in groups |
| Amount | £6,500 (GBP) |
| Organisation | International Centre for Mathematical Sciences (ICMS) |
| Sector | Academic/University |
| Country | United Kingdom |
| Start | 05/2014 |
| End | 07/2014 |