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PartAct SIGNED

Partial actions of monoids and partial reflections

Total Cost €

EC-Contrib. €

Partnership

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PartAct project word cloud

Explore the words cloud of the PartAct project. It provides you a very rough idea of what is the project "PartAct" about.

conjectures action theory answer notion lattices proving training universe algebras algebraic er inverse structure patterns always monoids methodology computation constructs weaving reflection feeding bijections journal corresponding monoid months symmetry mathematics spotting associative careful additional structures ideals skills constructed social constituents question act semigroup sciences scientists paradigm academic congruences designed totally mathematical achievements theoretical obj heart construct examples groups lift of actions encode lifted techniques output symmetric pure explore partial plan group personal situations correct approximately familiar usual

Project "PartAct" data sheet

The following table provides information about the project.

Coordinator	UNIVERSITY OF YORK Organization address address: HESLINGTON city: YORK NORTH YORKSHIRE postcode: YO10 5DD website: http://www.york.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.
Coordinator Country	United Kingdom [UK]
Total cost	183˙454 €
EC max contribution	183˙454 € (100%)
Programme	1. H2020-EU.1.3.2. (Nurturing excellence by means of cross-border and cross-sector mobility)
Code Call	H2020-MSCA-IF-2017
Funding Scheme	MSCA-IF-EF-ST
Starting year	2019
Duration (year-month-day)	from 2019-01-01 to 2020-12-31

Partnership

Take a look of project's partnership.

#	participants	country	role	EC contrib. [€]
1	UNIVERSITY OF YORK UNIVERSITY OF YORK Organization address address: HESLINGTON city: YORK NORTH YORKSHIRE postcode: YO10 5DD website: http://www.york.ac.uk contact info title: n.a. name: n.a. surname: n.a. function: n.a. email: n.a. telephone: n.a. fax: n.a.	UK (YORK NORTH YORKSHIRE)	coordinator	183˙454.00

Map

Project objective

Mathematics is at the heart of many areas of research in the Sciences and Social Sciences, with new mathematical achievements feeding the growth of other areas. Most scientists are familiar with the notion of the algebraic construct of a group, and how groups may be used to encode and explore the notion of symmetry, by studying the way on which they act on various structures. However, much of the universe is not symmetric, and neither do we always have actions totally known or defined. In such situations it is monoids, and partial actions, that provide the correct mathematical paradigm. The overall aim of this project is to develop and apply two (related) sets of semigroup theoretical techniques for actions and partial actions.

We have four sets of Objectives:

Obj. 1. To determine when the partial action of a monoid M on a set X via partial bijections can be lifted to actions by bijections, and answer the corresponding question for inverse monoids. Obj. 2. To determine the conditions under which strong partial actions of monoids on sets with additional structure lift to actions on sets with the same structure. Obj. 3. To develop the theory of associative algebras and C*-algebras constructed from (partial) monoid actions. Obj.4. To determine the algebraic constituents and constructs associated to reflection monoids, in particular, to determine their congruences and ideals, and associated lattices.

Each Objective is supported by a Work Package, each of which will take approximately 6 months, and result in a journal output. Our methodology, as usual in pure mathematics, is that of testing examples (including by computation), spotting patterns of behaviour, making and proving conjectures. A careful plan has been designed for the ER, weaving the academic objectives of the proposal with a 2 year programme of training and personal development in both skills and knowledge.

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The information about "PARTACT" are provided by the European Opendata Portal: CORDIS opendata.