## A-Infinity Algebras in Representation Theory (2001)

Citations: | 6 - 0 self |

### BibTeX

@MISC{Keller01a-infinityalgebras,

author = {Bernhard Keller},

title = {A-Infinity Algebras in Representation Theory},

year = {2001}

}

### OpenURL

### Abstract

We give a brief introduction to A1-algebras and show three contexts in which they appear in representation theory: the study of Yoneda algebras and Koszulity, the description of categories of ltered modules and the description of triangulated categories. Contents 1. Denitions, the bar construction, the minimality theorem 1 2. Yoneda algebras, Koszulity and ltered modules 5 3. Description of triangulated categories 8 References 10 1. Definitions, the bar construction, the minimality theorem 1.1. A-innity algebras and morphisms. We refer to [11] for a list of references and a topological motivation for the following denition: Let k be a eld. An A1 - algebra over k is a Z-graded vector space A = M p2Z A p endowed with graded maps (=homogeneous k-linear maps) mn : A