tau-tilting theory and the Brauer-Thrall conjectures

Abstract: Back in the 1940's, Brauer and Thrall announced two important results concerning the indecomposable representations of algebras. Since no proof was published in the years that followed the announcement, these statements started to be known as the first and second Brauer-Thrall conjectures. Many tools were introduced in representation theory in order to prove these conjectures and many years passed until a proof of these results was published.

In this talk we will start by motivating the conjectures from basic representation theory. Afterwards, we will show how recent results in tau-tilting theory give rise to modern versions of these conjectures, namely the first and second tau-Brauer-Thrall conjectures, and we will give a proof of the first tau-Brauer-Thrall conjecture.

Time permitting, we will discuss the second tau-Brauer-Thrall conjecture for special biserial algebras.

This is joint work with Sibylle Schroll and Yadira Valdivieso.

commutative algebraalgebraic geometryrings and algebrasrepresentation theory

Audience: researchers in the topic

Leeds algebra seminar

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