Introduction
Project
Members
Activities
Recent Publications
PhD
.
Contact
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Welcome
to the website of the research
group on Topological Groups at
the Department of
Physics and Applied Mathematics of the University
of Navarra.
Introduction
During
the
last century, Pontryagin
duality has been shown to be a
powerful tool for the analysis
of the structure and properties
of locally compact Abelian groups (LCA
groups).
These groups lie in the roots of Fourier Analysis, by means of the Haar
Measure and Bochner's theorem.
Pontryagin
duality on LCA groups acts as a mirror reflecting the properties of a
group on
its dual group (which is also locally compact), and conversely. This
motivates the
study of larger classes of groups
that
also satisfy Pontryagin duality (called reflexive groups).
Duality on broader
classes than LCA groups has been approached with diverse techniques and
scopes.
Some
particular research lines that our group has pursued
- Extend
the class of groups that satisfy Pontryagin duality.
- Study
the relations between algebraic and topological properties of a group
and its dual.
- Study
the topologies compatible with duality on different classes of
groups.
- Explore
the analogies between classical duality theory of topological vector
spaces, and topological groups.
We are currently developing the research project entitled: "Topological
groups, subgroups of topological vector spaces and compact groups."
ref:
MTM2006-03036 funded
by the Spanish Ministery of Science and Technology
Project Members
At the University of Navarra:
Other members:
- Vaja Tarieladze. Researcher
at Niko
Muskelishvili Institute of Computational Mathematics, Georgia
Activities
Future:
Recent
publications (members at the University of Navarra.)
- M. J.
Chasco,
E.
Martín Peinador, An
approach to duality on Abelian
precompact
groups. Journal of Group
Theory 11 (2008) 635-643.
- S.
Ardanza-Trevijano, M. J. Chasco, X. Domínguez, The
Role
of
Real
Characters in the Pontryagin Duality of Topological Abelian Groups.
Journal
of Lie Theory
18, pp 193-203
(2008).
- S.
Ardanza-Trevijano and M.J. Chasco, Continuous
convergence and duality
of limits of topological Abelian groups. Boletín
de la SMM
3a.
Serie. 13, pp 15-23 (2007).
- M.J.
Chasco, E. Martín-Peinador, V. Tarieladze, A
class of
angelic
sequential non-Fréchet Urysohn Topological Groups Topology
and
its
Applications 154, pp 741-748 (2007).
- L.
Ausenhofer, M. J. Chasco, X. Domínguez and V. Tarieladze,
On
Schwartz
groups. Studia Math. 181,
pp 199-210.
(2007).
- S.
Ardanza-Trevijano
and M.J. Chasco The
Pontryagin
duality of sequential limits of
topological Abelian groups. J.
Pure Appl. Algebra, 202, pp. 11-21, (2005).
top
PhD
Our
group is currently accepting PhD students. Candidates should have a
Master Degree in mathematics and a solid background in General
Topology , Abstract Algebra and Functional Analysis. If you are
interested please contact us.
Contact
If you would
like to contact us, please
send an e-mail to María
Jesús Chasco
or Sergio
Ardanza-Trevijano
Postal Adress:
Departamento de Fisica y Matematica Aplicada
Universidad de Navarra
C/ Irunlarrea S.N.
31080 Pamplona, Spain
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