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

CIBILS, CLAUDE; MARIA JULIA REDONDO; SOLOTAR, ANDREA

INDIANA UNIVERSITY MATHEMATICS JOURNAL

INDIANA UNIV MATH JOURNAL

Año: 2021 p. 1 - 28

0022-2518

Let 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 Λ is triangular with respect to a system of non necessarily primitive idempotents, and if the algebras at the idempotents belong to H, then is in H. Secondlywe consider a 2×2 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 H, then the algebra itself is in H.