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# Homology, Homotopy and Applications

## Volume 7 (2005)

### Number 2

### Proceedings of a Special Session of a Joint RSME-AMS Meeting at Sevilla University

### Free homotopy algebras

Pages: 123 – 137

DOI: http://dx.doi.org/10.4310/HHA.2005.v7.n2.a7

#### Author

#### Abstract

An explicit description of free strongly homotopy associative and free strongly homotopy Lie algebras is given. A variant of the Poincaré-Birkhoff-Witt theorem for the universal enveloping $A(m)$-algebra of a strongly homotopy Lie algebra is formulated.

#### Keywords

free algebra, $A(m)$-algebra, $L(m)$-algebra, PBW theorem

#### 2010 Mathematics Subject Classification

Primary 18D50. Secondary 17B35.