Skew Calabi-Yau triangulated categories and Frobenius Ext-algebras
  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. 
Manuel Reyes, Daniel Rogalski, James J. Zhang
math.RA math.CT