# Derivations of homotopy algebras

## Tom Lada and Melissa Tolley

Address: Department of Mathematics, North Carolina State University, Raleigh, NC 27695

E-mail:

lada@math.ncsu.edu

mmtolley@ncsu.edu

Abstract: We recall the definition of strong homotopy derivations of $A_\infty $ algebras and introduce the corresponding definition for $L_\infty $ algebras. We define strong homotopy inner derivations for both algebras and exhibit explicit examples of both.

AMSclassification: primary 18G55.

Keywords: L_\infty algebra, A_\infty algebra, strong homotopy derivation.

DOI: 10.5817/AM2013-5-309