Thirty-Third Annual Victorian Algebra Conference, Sydney, Australia, 2015

Register for: VAC33

Details of talk

TitleNon-commutative projective lines and bimodule species
PresenterDaniel Chan (University of New South Wales)
Author(s)Assoc Daniel Chan
Sessionn/a
Time
Abstract


In the 1970s, Beilinson discovered a beautiful derived equivalence between the
projective line and a certain finite-dimensional algebra called the Kronecker
algebra. This allows one to understand the representation theory of the
Kronecker algebra geometrically. The Kronecker algebra was generalised by Ringel
to bimodule species by replacing the two-dimensional vector space with a
bimodule of dimension two on either side. Non-commutative versions of the
projective line appeared with the work of Van den Bergh, Patrick and Nyman in
the 1990s and they also were constructed from such a bimodule. In this talk, we
will examine these non-commutative projective lines and show how they can shed
light on bimodule species. This is joint work with Adam Nyman.