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Article Dans Une Revue Indiana University Mathematics Journal Année : 2021

Han's conjecture and Hochschild homology for null-square projective algebras

María Julia Redondo
  • Fonction : Auteur
Andrea Solotar
  • Fonction : Auteur
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Résumé

Let $\mathcal H$ be the class of algebras verifying Han's conjecture. In this paper we analyse two types of algebras with the aim of providing an inductive step towards the proof of this conjecture. Firstly we show that if an algebra $\Lambda$ is triangular with respect to a system of non necessarily primitive idempotents, and if the algebras at the idempotents belong to $\mathcal H$, then $\Lambda$ is in $\mathcal H$. Secondly we consider a $2\times 2$ matrix algebra, with two algebras on the diagonal, two projective bimodules in the corners, and zero corner products. They are not triangular with respect to the system of the two diagonal idempotents. However, the analogous result holds, namely if both algebras on the diagonal belong to $\mathcal H$, then the algebra itself is in $\mathcal H$.

Dates et versions

hal-01812730 , version 1 (11-06-2018)

Identifiants

Citer

Claude Cibils, María Julia Redondo, Andrea Solotar. Han's conjecture and Hochschild homology for null-square projective algebras. Indiana University Mathematics Journal, 2021, 70 (2), pp.639-668. ⟨10.1512/iumj.2021.70.8402⟩. ⟨hal-01812730⟩
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