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arXiv · 2303.17369

Strongly stratifying ideals, Morita contexts and Hochschild homology

Claude Cibils·Marcelo Lanzilotta·Eduardo N. Marcos·Andrea Solotar
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Abstract

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.

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Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, Andrea Solotar. 2023-10-12. Strongly stratifying ideals, Morita contexts and Hochschild homology. https://arxiv.org/abs/2303.17369

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