Invariant ideals in Leavitt path algebras

Abstract: As well-known examples of Leavitt path algebras arise the so-called primary colours: they respectively correspond to the ideal generated by the set of line points, the vertices that lie on cycles without exits and the one generated by the set in extreme cycles. It is known that these ideals are invariant under isomorphism. In this talk we will analyze the invariance of another key piece of a Leavitt path algebra. We will see that though the ideal generated by the vertices whose tree contains infinitely many bifurcation vertices or at least one infinite emitter is not invariant, we will find its natural replacement (which is indeed invariant). We will also give some procedures to construct invariant ideals from previous known invariant ideals. In order to do that, on the one hand, we will introduce a topology in the set of vertices of a graph. And on the other hand, via category theory, we will think of the saturated and hereditary set of a graph as a functor. This a joint work together with Dolores Martín Barquero and Cándido Martín González.

operator algebrasrings and algebras

Audience: researchers in the topic

Western Sydney University Abend Seminars

Series comments: Description: Western Sydney University Abend Seminars

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