Courses

Department of Mathematical Sciences

Institutt for matematiske fag

Alfred Getz' vei 1, 7. etasje

NTNU Gløshaugen

7034 Trondheim. Norway

bergh@math.ntnu.no

http://www.math.ntnu.no/~bergh/

Hochschild cohomology and homology of algebras (6-hours course)

Hochschild cohomology was introduced by Gerhard Hochschild in 1945. Together with Hochschild homology, it has become a useful tool for studying the structure of associative algebras. In this series of talk, we will introduce these concepts, starting from scratch. We will illustrate the theory with numerous examples

María Guadalupe Corrales García, José Félix Solanilla Hernández

(members of the Scientific Committee and of the Organizing Committee)

Centro Regional Universitario de Coclé “Dr. Bernardo Lombardo”

Universidad de Panamá

Apartado Postal 0229

Penonomé, Coclé. Panamá

mcorrales@up.ac.pa, jose.solanilla@up.ac.pa

An introduction to Leavitt path algebras (6-hours course)

This course will start by introducing certain topics about the algebras and graph theory

which is necessary to explain the construction of Leavitt path algebras. Some fundamental examples will follow together with the relation to Bergman and graph C*-algebras. In addition, connections to other graph algebras such as Cohn path algebras will be discussed.

The description of (graded) ideals will be exhibited and shown to play a fundamental role in the structure of these algebras; in particular, the socle, the ideal generated by elements in cycles without exits and the recently described ideal generated by vertices in extreme cycles, will be crucial for this end. These ideals will be useful also to compute the center of a Leavitt path algebra.

The remarkable, close inter-connection between properties of the graph and algebraic properties of the associated algebra will be examined. The discussion will be enhanced by historical remarks.

Karin Erdmann

Mathematical Institute

24-29 St. Giles, Oxford OX1 3LB, UK

erdmann@maths.ox.ac.uk

https://people.maths.ox.ac.uk/erdmann/

Root systems and representation theory

We introduce root systems and discuss the classification via Dynkin diagrams.

We describe how root systems and Dynkin diagrams occur in representation theory of associative algebras, and how they are related to finiteness conditions. Specifically we will consider finite-dimensional path algebras of quivers, but also Frobenius algebras with radical cube zero, and as well preprojective algebras.

Mercedes Siles Molina

(member of the Scientific Committee)

Departamento de Álgebra, Geometría y Topología

Universidad de Málaga

29071 Málaga

Spain

msilesm@uma.es

http://webpersonal.uma.es/~MSILESM/

The Lie structure of a Leavitt path algebra (6-hours course)

This course will be devoted to study Leavitt path algebras but considered as Lie algebras with the product given by the commutator. We will start with the description of the center of a Leavitt path algebra L=L_K(E). Then we will be in position to characterize the simplicity of the Lie algebra [L, L]/Z([L, L]), for Z() the center. Another interesting objective will be the description of the Lie ideals of L. We will speak about the state of the art of this topic and some related open problems.

Conferences

Claude Cibils

(member of the Scientific Committee)

http://www.math.univ-montp2.fr/~cibils/

Free Invariants (one-hour conference)

Cándido Martín González

(member of the Scientific Committee)

http://agt2.cie.uma.es/

An introduction to the Lorentz algebra (one-hour conference)

Dolores Martín Barquero

http://www.matap.uma.es/~dmartin/

An introduction to the Lorentz Group (one-hour conference)

Daniel Labardini Fragoso

http://www.matem.unam.mx/labardini/

Algebras from triangulations of surfaces (two one-hour sessions)

I will present a construction that associates an algebra to each triangulation of a surface with marked points and is well behaved under an elementary combinatorial move called flip.

Surfaces with marked points and orbifold points arise when one considers quotients of the hyperbolic plane by the action of discrete subgroups of PSL_2(R). Felikson-Shapiro-Tumarkin have associated valued quivers to the triangulations of a surface with marked points and orbifold points of order 2. In this lecture I will show how to associate algebras to these triangulations in a way that is well behaved under flips. This talk is based on joint work in progress with Jan Guenich.

Andrea Solotar

http://mate.dm.uba.ar/~asolotar/

Rewriting methods and resolutions of associative algebras (two one-hour sessions)

	Mond.	Tuesd.	Wedn.	Thursd.	Frid.	Mond.	Tuesd.	Wedn.
09:00-09:50	KE	KE	KE	KE	KE	KE	KE	PAB
10:00-10:50	%%%%	%%%%	%%%%	%%%%	%%%%	%%%%	%%%%	MSM
10:50-11:20	Coffee break
11:20-12:10	MGC/JFS	MGC/JFS	MGC/JFS	MGC/JFS	MGC/JFS	MGC/JFS	MGC/JFS	Lect. or Q & E
	Lunch
14:00-14:50	PAB	PAB		PAB	PAB	PAB	PAB
15:00-15:50	MSM	MSM		MSM	MSM	MSM	MSM
15:50-16:10	Break			Break
16:10-17:30	Lect. or	Lect. or		Lect. or	Lect. or	Lect. or	Lect. or
	Q & E	Q & E		Q & E	Q & E	Q & E	Q & E

PAB = Petter Andreas Bergh

MGC = María Guadalupe Corrales García

KE = Karin Erdmann

MSM = Mercedes Siles Molina

%%%% = Undecided

JFS= José Félix Solanilla Hernández

Lect. or Q & E = Lectures by our invited speakers, or questions and exercises.

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