Title: Finite Dimensional Algebras and the Preprojective Algebra of a Quiver TBA

2014.04.15 |

Date | Wed 30 Apr |

Time | 15:30 — 16:30 |

Location | Aud. D3 |

**Abstract**

My talk will be about representation theory of finite dimensional algebras. I will start by giving an introduction to the theory focusing on the case when the algebra is hereditary. In particular I will explain why it is sufficient to only study path algebras. Hopefully I will also have time to mention Gabriels theorem.

The second part of my talk will be about the preprojective algebra of a quiver. It can be shown that the preprojective algebra is isomorphic to the tensor algebra of some bimodule. This implies that it has a homological definition, which makes it easy to generalize. If time permits I will also give an indication of how the preprojective algebra can be considered as the 2-Calabi-Yau completion of the path algebra of the underlying quiver.