#### Title

Separated Lie Models and the Homotopy Lie Algebra

#### Document Type

Article

#### Publication Date

2-2008

#### Publication Title

Journal of Pure and Applied Algebra

#### Abstract

A simply connected topological space *Formula Not Shown* has homotopy Lie algebra *Formula Not Shown* . Following Quillen, there is a connected differential graded free Lie algebra (dgL) called a Lie model, which determines the rational homotopy type of *Formula Not Shown* , and whose homology is isomorphic to the homotopy Lie algebra. We show that such a Lie model can be replaced with one that has a special property that we call being *separated*. The homology of a separated dgL has a particular form which lends itself to calculations. c2007 Elsevier B.V. All rights reserved.

#### Repository Citation

Bubenik, P., (2008). Separated Lie models and the homotopy Lie algebra. Journal of Pure and Applied Algebra, 212(2), 401-410.

#### Original Citation

Bubenik, P., (2008). Separated Lie models and the homotopy Lie algebra. Journal of Pure and Applied Algebra, 212(2), 401-410.

#### DOI

10.1016/j.jpaa.2007.05.018

#### Volume

212

#### Issue

2