English

A-infinity algebras, modules and functor categories

Representation Theory 2007-05-23 v3 Rings and Algebras

Abstract

In this survey, we first present basic facts on A-infinity algebras and modules including their use in describing triangulated categories. Then we describe the Quillen model approach to A-infinity structures following K. Lefevre's thesis. Finally, starting from an idea of V. Lyubashenko's, we give a conceptual construction of A-infinity functor categories using a suitable closed monoidal category of cocategories. In particular, this yields a natural construction of the bialgebra structure on the bar construction of the Hochschild complex of an associative algebra.

Keywords

Cite

@article{arxiv.math/0510508,
  title  = {A-infinity algebras, modules and functor categories},
  author = {Bernhard Keller},
  journal= {arXiv preprint arXiv:math/0510508},
  year   = {2007}
}

Comments

errors in section 5.1 corrected, references added, 27 pages