Han's conjecture for bounded extensions

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.

arXiv commentUpdated version. We have replaced the misleading "smooth algebra" by the standard "algebra of finite global dimension". The Appendix is now incorporated in a more direct and shorter form at Section 5

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