Rigidity of higher Auslander algebras of type \mathbbA

2026/07/27 by Sibylle Schroll, Andrea Solotar, Can Wen
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Abstract

We show that the Hochschild cohomology of higher Auslander algebras of type \mathbbA vanishes in all positive degrees and is one-dimensional in degree zero. As a consequence, these algebras are rigid and intrinsically formal.

Citations

• Fractionally Calabi-Yau lattices that tilt to higher Auslander algebras of type A
• Hochschild (co)homology dimension

Related

• Higher gentle algebras
• Rigidity dimension - a homological dimension measuring resolutions of algebras by algebras of finite global dimension
• Maximal rigid modules over a gentle algebra and applications to higher Auslander-Reiten theory
• Deformations associated to rigid algebras
• An Auslander-Buchsbaum formula for higher Auslander algebras and applications