$\tau$-tilting finiteness of two-point algebras II

Qi Wang

$\tau$-tilting finiteness of two-point algebras II

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arxiv 2206.00239 v2 pith:ZBTQHDPU submitted 2022-06-01 math.RT

Qi Wang This is my paper · ORCID

classification math.RT

keywords algebrastiltingtwo-pointalgebrafinitenesscasesclassconsequently

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abstract

In this paper, we explain a strategy on $g$-vectors to discover some new minimal $\tau$-tilting infinite two-point algebras. Consequently, the $\tau$-tilting finiteness of various two-point monomial algebras, including all radical cube zero cases, could be determined. Moreover, we find that the derived equivalence class of the Kronecker algebra contains only itself and its opposite algebra.

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Fans and polytopes in tilting theory III: Classification of convex $g$-fans of rank 3
math.RT 2025-08 conditional novelty 6.0 of 10

For rank 3, there are exactly 61 convex g-fans up to isomorphism, and each is determined by a simple numerical invariant of the algebra.

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