Seminari di Algebra del giorno 11 giugno 2014

- Ore 10:00, Aula Aula Benvenuti

Relatore: Prof. Alberto Elduque, Università di Saragozza

Titolo: Fine gradings and gradings by root systems on simple Lie algebras

- Ore 11:00, Aula Aula Benvenuti

Relatore: Prof.ssa Mercedes Siles Molina, Università di Malaga

Titolo: Extreme cycles. The center of a Leavitt path algebra.

Abstract: In this talk we will speak about the new techniques we introduce in order to deepen into the structure of a Leavitt path algebra with the aim of giving a description of its center when the graph is row-finite. In particular, we will address our attention to the extreme cycles, which appear for the first time in the literature; they concentrate the purely infinite part of a Leavitt path algebra. Jointly with the line points and the vertices in cycles without exits, they are the key ingredients to

determine the center. Our work will rely on our previous approach to the center of a prime Leavitt path algebra. We will go further into the structure itself of the Leavitt path algebra. For example, the ideal $I(P_{ec} \cup P_{c} \cup P_l)$ generated by vertices in extreme cycles ($P_{ec}$), by vertices in cycles without exits ($P_c$) and by line points ($P_l$) will be a dense ideal in some cases, for instance in the finite one or, more generally, if every vertex connects to $P_l \cup P_c\cup

P_{ec}$. Hence its structure will contain much of the information about the Leavitt path algebra. To deal with row-finite graphs, we will need to add a new hereditary set: the set of vertices whose tree has infinite bifurcations ($P_{b^\infty}$).

This is a joint work with Maria Guadalupe Corrales Garcia, Dolores Martin Barquero, Candido Martin Gonzalez and Jose Felix Solanilla Hernandez.

Referente: F. Catino