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Accueil > Écoles de recherche > Ecoles de recherche 2015 > Liste chronologique des écoles de recherche 2015 > Non-commutative Algebra

Non-commutative Algebra

English Version

CIMPA-PANAMA research school

Centro Regional Universitario de Coclé, October 19-28, 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.

Administrative and scientific coordinators

- José Félix Solanilla Hernández (Universidad de Panamá) jose.solanilla@up.ac.pa
- Cándido Martín González (Universidad de Málaga Spain) candido@apncs.cie.uma.es

Scientific Committee

  • Claude Cibils (Université Motpellier 2, France)
  • María Guadalupe Corrales García (Universidad de Panamá en Coclé, Panama)
  • Cándido Martín González (Universidad de Málaga, España)
  • Mercedes Siles Molina (Universidad de Málaga, España)
  • José Félix Solanilla Hernández (Universidad de Panamá en Coclé, Panamá)

Local Organizing Committee

  • Idulfo Arrocha Rodríguez
  • María Guadalupe Corrales García
  • Ariscela Díaz Iturralde
  • Jaime Gutiérrez González
  • José Félix Solanilla Hernández
  • Javier Torres Salgado

Scientific Program

Courses

  • Petter Andreas Bergh (Trondheim, Norway) : Hochschild cohomology and homology of algebras (6-hours course)
  • María Guadalupe Corrales García, José Félix Solanilla Hernández (Universidad de Panamá) : An introduction to Leavitt path algebras (6-hours course)
  • Karin Erdmann (Oxford, UK) : Root systems and representation theory (6-hours course)
  • Mercedes Siles Molina (Universidad de Málaga, Spain) : The Lie structure of a Leavitt path algebra (6-hours course)
  • Andrea Solotar (Buenos Aires, Argentina) (3-hours courses)
  • Daniel Labardini Fragoso (Mexico) (3-hours courses)

Conferences

  • Claude Cibils (Member of the Scientific Committee) : Free invariants (one-hour conference)
  • Cándido Martín González (Member of the Scientific Committee) : The gauge action of a Leavitt path algebra (one-hour conference)

Deadline for registration

August 30, 2015

Application procedure only for applicants not from Panama.

Applicants from Panama must contact local organizer : Ariscela Díaz Iturralde (ariscela11@gmail.com)

Voir en ligne : Local web site