Algebra Seminar: Chan -- 2-hereditary algebras and almost Fano weighted projective surfaces

Daniel Chan (University of New South Wales) 

Friday 24 June, 12-1pm, Place: Carslaw 375 

2-hereditary algebras and almost Fano weighted projective surfaces

Tame hereditary algebras are a classical objects of study in the 
representation theory of finite dimensional algebras. They include 
path algebras of extended Dynkin quivers as examples. In the 1980’s, 
Geigle and Lenzing gave an intriguing approach to studying their 
representation theory by showing that, up to Morita equivalence, 
they are classified by certain non-commutative analogues of the 
projective line, namely the Fano weighted projective lines. 
Furthermore, the nice representation theory of tame hereditary 
algebras could be deduced from the nice module theory of the 
corresponding weighted line via tilting theory. In this talk, we will 
examine a dimension 2 generalisation of this picture as introduced 
by Iyama and his school in the last decade.