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arXiv · 2509.04990

Virtually Gorenstein algebras of infinite dominant dimension

Hongxing Chen·Changchang Xi
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Abstract

Motivated by understanding the Nakayama conjecture which states that algebras of infinite dominant dimension should be self-injective, we study self-orthogonal modules with virtually Gorenstein endomorphism algebras and prove the following result: Given a finitely generated, self-orthogonal module over an Artin algebra with an orthogonal condition on its Nakayama translation, if its endomorphism algebra is virtually Gorenstein, then the module is projective. As a consequence, we re-obtain a recent result: the Nakayama conjecture holds true for the class of strongly Morita, virtually Gorenstein algebras. Finally, we show that virtually Gorenstein algebras can be constructed from Frobenius extensions.

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Hongxing Chen, Changchang Xi. 2025-09-05. Virtually Gorenstein algebras of infinite dominant dimension. https://arxiv.org/abs/2509.04990

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