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Pré-Publication, Document De Travail Année : 2023

Strongly stratifying ideals, Morita contexts and Hochschild homology

Marcelo Lanzilotta
  • Fonction : Auteur
Eduardo N. Marcos
  • Fonction : Auteur
Andrea Solotar
  • Fonction : Auteur

Résumé

We consider stratifying ideals of finite dimensional algebras in relation with Morita contexts. A Morita context is an algebra built on a data consisting of two algebras, two bimodules and two morphisms. For a strongly stratifying Morita context - or equivalently for a strongly stratifying ideal - we show that Han's conjecture holds if and only if it holds for the diagonal subalgebra. The main tool is the Jacobi-Zariski long exact sequence. One of the main consequences is that Han's conjecture holds for an algebra admitting a strongly (co-)stratifying chain whose steps verify Han's conjecture. If Han's conjecture is true for local algebras and an algebra admits a primitive strongly (co-)stratifying chain, then Han's conjecture holds for it.

Dates et versions

hal-04053785 , version 1 (31-03-2023)

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Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, Andrea Solotar. Strongly stratifying ideals, Morita contexts and Hochschild homology. 2023. ⟨hal-04053785⟩
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