有界扩张的Han猜想
Han's conjecture for bounded extensions
摘要：
设$B\subset A$是有限维代数的左或右有界扩张.本文利用Jacobi-Zagliki长近正合序列证明了$B$满足Han猜想的充要条件是$A$满足Han猜想，而不管扩张是否分裂.我们提供的条件，确保箭头和关系的延伸是左或右有界的。最后，我们给出了一个由可容许关系和可容许关系给出的代数扩张的结构结果，并给出了非分裂左、右有界扩张的例子。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
