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Система компьютерной алгебры GAP

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Сайт рассылки: http://www.gap-system.org/ukrgap/
Открыта: 05-02-2002

Автор
Александр Борисович Коновалов

Статистика

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Система компьютерной алгебры GAP - Mini-workshop on algebra


CENTRO DE ALGEBRA DA UNIVERSIDADE DE LISBOA
http://caul.cii.fc.ul.pt/

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* MINI-WORKSHOP ON ALGEBRA *
****************************

DIA 18 DE ABRIL DE 2008 (SEXTA-FEIRA), 14H30M, ANFITEATRO


"Universal algebra and CSP" by Catarina Carvalho (CAUL, Portugal)

Abstract: I 'll introduce the subject of Constraint Satisfaction Problems (CSP)
and relate the study of its complexity  with Universal Algebra.


"Approaching cosets using Green's relations and Schutzenberger groups" by
Robert Gray (University of St. Andrews, U.K.)

Abstract: One of the most fundamental concepts in combinatorial group
theory is the notion of index. The index of a subgroup is found by counting
its right (or left) cosets. It may be thought of as providing a way of
measuring the difference between a group and a subgroup. In this sense, we
can think of finite index subgroups as only differing from their parent
group by a finite amount. Many finiteness conditions are known to be
preserved under taking finite index subgroups and extensions, including:
finite generation / presentability, periodicity, local finiteness, residual
finiteness, and having a soluble word
problem. Over the past decade or so, several attempts have been made to
develop an analogous theory of index for semigroups. In my talk I shall
discuss two such
approaches (and some recent results relating to them) which arise from two
different ways of thinking about what coset should mean for semigroups. The
first approach is to think of cosets as being right translates of the
substructure under the action of the semigroup on subsets. This approach is
restricted in the sense that it only applies usefully to subgroups of
semigroups (and not arbitrary subsemigroups). The second approach is a
notion of index (which is called the Green index) that arises from a
generalised form
of Green's relations, where Green's relations are taken relative to a given
subsemigroup. This approach has the advantage that it applies to arbitrary
subsemigroups. In both cases, theorems exist relating the properties of the
semigroup, its subsemigroups, and certain Schutzenberger groups.


"Partial Actions of Inverse Monoids on K-Rings" by Christopher Hollings
(CAUL, Portugal)

Abstract: The partial actions of groups on K-rings (a.k.a. associative
K-algebras) have been studied by Dokuchaev and Exel (2005), as a purely
algebraic version of earlier work on the partial actions of groups on
C*-algebras.
In particular, Dokuchaev and Exel address the perennial problem of
constructing an action from a partial action, which in this case is termed
the 'enveloping action' of the given partial action. In this talk, I will
set up appropriate definitions for the partial actions of inverse monoids
on K-rings and describe the construction of enveloping actions for such
partial actions.


LOCAL:
Complexo Interdisciplinar da Universidade de Lisboa
Av. Prof. Gama Pinto 2
1649-003 Lisboa
Portugal
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