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arXiv · 2101.02597

Han's conjecture for bounded extensions

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

Let $B\subset A$ be a left or right bounded extension of finite dimensional algebras. We use the Jacobi-Zariski long nearly exact sequence to show that $B$ satisfies Han's conjecture if and only if $A$ does, regardless if the extension splits or not. We provide conditions ensuring that an extension by arrows and relations is left or right bounded. Finally we give a structure result for extensions of an algebra given by a quiver and admissible relations, and examples of non split left or right bounded extensions.

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Claude Cibils, Marcelo Lanzilotta, Eduardo N. Marcos, Andrea Solotar. 2021-01-07. Han's conjecture for bounded extensions. https://doi.org/10.1016/j.jalgebra.2022.01.022

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