John MacQuarrie

Extensions of algebras preserving some homological properties

An extension of algebras is (for us) an associative algebra A with a subalgebra B. In a sequence of articles, Claude Cibils, Marcelo Lanzilotta, Eduardo Marcos and Andrea Solotar consider a class of extensions of algebras and prove that the finitude of the global dimension and of the support of the Hochschild homology are preserved by these extensions, so that in particular Han's Conjecture holds for B iff it holds for A. Working with Kostiantyn Iusenko, we consider a more general class of extensions (better suited to the algebras that interest us) and prove that the same homological finiteness properties are preserved. We also add a further property: the finiteness of FinDim, to the list.