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This is a Quantitative Study study.

October 3, 2025Open Access

Happel's question, Han's conjecture and $τ$-Hochschild (co)homology

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The study links the τ-Hochschild (co)homology to the global dimension of finite dimensional algebras, revealing important relationships.
It also explores the connections between τ-Hochschild (co)homology and significant conjectures such as Happel's question and Han's conjecture.
The introduction of higher Auslander-Reiten translates provides a new perspective on τ-Hochschild (co)homology in associative algebra.
Findings may influence future research on algebra properties and deepen understanding of related theories.

Implication

This analysis connects τ-Hochschild (co)homology with global dimension and conjectures by Happel and Han.

Abstract

We introduce the $τ$-Hochschild (co)homology of a finite dimensional associative algebra $Λ$ by means of the higher Auslander-Reiten translate of O. Iyama. We show that the global dimension of $Λ$, Happel's question and Han's conjecture are related to the $τ$-Hochschild (co)homology.

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Cite This Study

Cibils et al. (2025) studied this question.

synapsesocial.com/papers/68e02f46f0e39f13e7fa2e92 https://doi.org/10.48550/arxiv.2509.05135

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Implication

This analysis connects τ-Hochschild (co)homology with global dimension and conjectures by Happel and Han.

Happel's question, Han's conjecture and $τ$-Hochschild (co)homology

Key Points

Implication

Abstract

Discussion

Cite This Study

Happel's question, Han's conjecture and $τ$-Hochschild (co)homology

Key Points

Implication

Abstract

Discussion

Cite This Study

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