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arXiv · 2607.15999

Bounds on Frobenius dimension

D. Artenstein·J. Cóppola·J. Finot·A. González·G. Mata
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Abstract

In this article, we prove two types of results about the Frobenius dimension of associative algebras. First, we refine the known upper bound for the Frobenius dimension of a finite dimensional algebra in terms of its dimension as a vector space, and show that the only algebras reaching this bound are radical square zero algebras associated with single-vertex quivers. Second, we compute Frobenius dimension for low-dimensional algebras explicitly, and for truncated path algebras in terms of paths with no detours in their underlying quivers.

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D. Artenstein, J. Cóppola, J. Finot, A. González, G. Mata. 2026-07-17. Bounds on Frobenius dimension. https://arxiv.org/abs/2607.15999

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