Algebras, Coalgebras, Homology

Abstract

In this chapter we recall elementary facts about algebras and homological algebra, essentially to establish the terminology and the notation. We first review the notions of associative, commutative and Lie algebra. Then we deal with the notion of coalgebra, which is going to play a key role in this book. This leads to the notion of convolution. The last sections cover bialgebras, pre-Lie algebras, differential graded objects and convolution algebra.