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Han's conjecture for bounded extensions

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arxiv 2101.02597 v3 pith:DMUVXOWO submitted 2021-01-07 math.KT math.ACmath.RAmath.RT

Claude Cibils , Marcelo Lanzilotta , Eduardo N. Marcos , Andrea Solotar This is my paper · ORCID
classification math.KTmath.ACmath.RAmath.RT
keywords boundedextensionextensionsleftrightconjecturerelationsadmissible
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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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  1. Protected corners and a trichotomy for Han's conjecture

    math.RT 2026-07 conditional novelty 7.0 of 10

    All three simples of a three-vertex Gap-A failure cannot all have infinite projective dimension; the two-infinite case is forced to be a 'mutual dumbbell', and a protected corner forces Ext^n(S_x,S_x) nonzero in every degree.

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