Using Haskell to study A-infinity algebras and bialgebras.
by
Mikael Vejdemo Johansson
Universität Jena

Strongly homotopy associative algebras, or A_∞-algebras were invented by Stasheff (1963), and have found uses both in topology and in representation theory since. A method, using a cellular diagonal on associahedra, for constructing tensor products of A_∞-algebras was found by Saneblidze and Umble (2004), and the theory has been recently generalized to A_∞-bialgebras by Umble.

We discuss the uses of the functional programming language Haskell in computing with A_∞ algebra tensor products and in searching for examples of A_∞ bialgebras. Several characteristics of Haskell turn out to be highly beneficial for these tasks - noticably the declarative style and the ease with which new algebraic datatypes can be constructed and used.

Date received: May 22, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caxd-27.