AI 中文总结
本文针对代数闭域上的有限表示型代数，证明了满足特定条件的自同态代数的嘉当行列式为1，从而验证了该类代数的嘉当行列式猜想成立。
AI 中文摘要
设A是代数闭域k上的有限维有限表示型代数，M是有限维A-模，满足End_A(M)具有有限整体维数。我们证明：若A具有有限整体维数或char k≠2，则End_A(M)的嘉当行列式为1；特别地，代数闭域上有限表示型代数的嘉当行列式猜想成立。
英文摘要
Let $A$ be a finite-dimensional representation-finite algebra over an algebraically closed field $k$, and let $M$ be a finite-dimensional $A$-module such that $\operatorname{End}_A(M)$ has finite global dimension. We prove that $\operatorname{End}_A(M)$ has Cartan determinant one if $A$ has finite global dimension or $\operatorname{char}k\neq2$; in particular, the Cartan determinant conjecture holds for representation-finite algebras over an algebraically closed field.
Comments5 pages, comments welcome!
