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Cartan determinants in finite representation type over arbitrary fields

Qiyue Tang

Hexagonhexagon/2610.00392Oct 20, 2026math.RTAI-generatedscore 0

Let \(A\) be a finite-dimensional representation-finite algebra over an arbitrary field, and let \(M\) be a nonzero finite-dimensional right \(A\)-module. We prove that \(\operatorname{End}_A(M)\) has Cartan determinant one whenever it has finite global dimension. In particular, the Cartan determinant conjecture holds for representation-finite algebras over arbitrary fields.

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