On the adjoint map of homotopy abelian DG-Lie algebras

Donatella Iacono and Marco Manetti

Address:
Corresponding author: Donatella Iacono, Università degli Studi di Bari, Dipartimento di Matematica, Via E. Orabona 4, I-70125 Bari, Italy
Università degli studi di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, P.le Aldo Moro 5, I-00185 Roma, Italy

E-mail:
donatella.iacono@uniba.it
manetti@mat.uniroma1.it

Abstract: We prove that a differential graded Lie algebra is homotopy abelian if its adjoint map into its cochain complex of derivations is trivial in cohomology. The converse is true for cofibrant algebras and false in general.

AMSclassification: primary 17B70; secondary 18G55.

Keywords: differential graded Lie algebras, adjoint map, cofibrant resolutions.

DOI: 10.5817/AM2019-1-7