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arXiv · 1709.05049

From support $\tau$-tilting posets to algebras

Ryoichi Kase
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Abstract

The aim of this paper is to study a poset isomorphism between two support $\tau$-tilting posets. We take several algebraic information from combinatorial properties of support $\tau$-tilting posets. As an application, we treat a certain class of basic algebras which contains preprojective algebras of type $A$, Nakayama algebras, and generalized Brauer tree algebras. We provide a necessary condition for that an algebra $\Lambda$ share the same support $\tau$-tilting poset with a given algebra $\Gamma$ in this class. Furthermore, we see that this necessary condition is also a sufficient condition if $\Gamma$ is either a preprojective algebra of type $A$, a Nakayama algebra, or a generalized Brauer tree algebra.

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Ryoichi Kase. 2017-09-15. From support $\tau$-tilting posets to algebras. https://arxiv.org/abs/1709.05049

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