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

Key Points

• 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.