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On the adjoint map of homotopy abelian DG-Lie algebras

Donatella Iacono, Marco Manetti (2019)

Archivum Mathematicum

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.

On the characterisation of Mal'tsev and Jónsson-Tarski algebras

Jonathan D.H. Smith (2003)

Discussiones Mathematicae - General Algebra and Applications

There are very strong parallels between the properties of Mal'tsev and Jónsson-Tarski algebras, for example in the good behaviour of centrality and in the factorization of direct products. Moreover, the two classes between them include the majority of algebras that actually arise 'in nature'. As a contribution to the research programme building a unified theory capable of covering the two classes, along with other instances of good centrality and factorization, the paper presents a common framework...

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