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The University of Panama- Centro Regional Universitario de Coclé jointly with the International Centre of
Applied and Pure Mathematic will celebrate the:
1st
CIMPA research school
-Non commutative algebra- at Coclé.
October, from 19 to 28, 2015
Non-commutative algebraic structures are at the core of
recent developments of fundamental mathematics, from quantum groups (Hopf
algebras) to non-commutative geometry. In this project of Research School
complementary aspects are considered inside this direction: homology and
cohomology, Frobenius algebras, representation theory and path algebras as well
as Leavitt path algebras. Those subjects as well as their articulations will
provide a first strong inside to the theory.
Homology and cohomology of algebras are useful tools in
various domains of mathematics; they are related to notions such as
the center, the derivations, rigidity and to several fundamental
conjectures for understanding associative algebraic structures. The corresponding
course will enable beginners to learn from the scratch the fundamental aspects.
Several examples will be considered too.
Frobenius algebras represent a wide class of algebras
containing several important classes including Hopf algebras. The course will
provide an elementary introduction to the theory, related to representation
theory.
Representation theory is an influential bunch
of mathematics, for instance it is strongly linked with particle physics. This goes hand
in hand with the representation theory of Lie groups and algebras, where the
notions of root system and Dynkin diagrams play a central role.
Precisely the course on root systems and representation
theory will introduce basic concepts and the classification via Dynkin diagrams.
It will show how Dynkin diagrams occurs in representation theory of finite
dimensional associative algebras (path algebras), and how this is related to
finiteness conditions on the number of indecomposable modules.
A course on path and Leavitt path algebras will also
take place. After introducing Leavitt path algebras the main concern will be the
Lie structure of Leavitt path algebras. The starting point will be the study of
the center of a Leavitt path algebra and then the study of the derived Lie
algebra modulo its center.
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