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arXiv · 2608.23132

The Cartan determinant conjecture for representation-finite algebras

Haruhisa Enomoto
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Abstract

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.

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Haruhisa Enomoto. 2026-08-24. The Cartan determinant conjecture for representation-finite algebras. https://arxiv.org/abs/2608.23132

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