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arXiv · 2406.16011

The derived dimensions and representation distances of artin algebras

Junling Zheng·Yingying Zhang
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Abstract

There is a well-known class of algebras called Igusa-Todorov algebras which were introduced in relation to finitistic dimension conjecture. As a generalization of Igusa-Todorov algebras, the new notion of $(m,n)$-Igusa-Todorov algebras provides a wider framework for studying derived dimensions. In this paper, we give methods for constructing $(m,n)$-Igusa-Todorov algebras. As an application, we present for general artin algebras a relationship between the derived dimension and the representation distance. Moreover, we end this paper to show that the main result can be used to give a better upper bound for the derived dimension for some classes of algebras.

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Junling Zheng, Yingying Zhang. 2024-06-23. The derived dimensions and representation distances of artin algebras. https://arxiv.org/abs/2406.16011

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