Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras

Abstract

We investigate the conditions that are sufficient to make the Ext-algebra of an object in a (triangulated) category into a Frobenius algebra and compute the corresponding Nakayama automorphism. As an application, we prove the conjecture that hdet(${\mu }_A$) = 1 for any noetherian Artin-Schelter regular (hence skew Calabi-Yau) algebra A.

31 pages

References in corpus (1)

• Calabi-Yau algebras

Cited by in corpus (16)

• Derived Categories
• Graded twisted Calabi-Yau algebras are generalized Artin-Schelter regular
• Note on Nakayama automorphisms of PBW deformations and Hopf actions
• On quantum groups associated to non-Noetherian regular algebras of dimension 2
• Cluster tilting modules and noncommutative projective schemes
• New Artin-Schelter regular and Calabi-Yau algebras via normal extensions
• Nakayama Automorphism and Rigidity of Dual Reflections Group Coactions
• Higher zigzag algebras
• Nakayama automorphism and applications
• Stable Categories of Graded Maximal Cohen-Macaulay Modules over Noncommutative Quotient Singularities
• Automorphism groupoids in noncommutative projective geometry
• Nakayama automorphisms of graded Ore extensions of Koszul Artin-Schelter regular algebras
• Nakayama automorphism of a class of graded algebras
• m-Koszul Artin-Schelter regular algebras
• The Jacobian, reflection arrangement and discriminant for reflection Hopf algebras
• Nakayama automorphisms of twisted tensor products