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Title: | Dualizing complexes of noetherian complete algebras via coalgebras | Authors: | He, J. -W. Torrecillas, B. Van Oystaeyen, F. ZHANG, Yinhuo |
Issue Date: | 2014 | Source: | COMMUNICATIONS IN ALGEBRA, 42 (1), p. 271-285 | Abstract: | Let A be a noetherian complete basic semiperfect algebra over an algebraically closed field, and C=A degrees be its dual coalgebra. If A is Artin-Schelter regular, then the local cohomology of A is isomorphic to a shift of twisted bimodule C-1(sigma*) with sigma a coalgebra automorphism. This yields that the balanced dualinzing complex of A is a shift of the twisted bimodule (sigma*)A(1). If sigma is an inner automorphism, then A is Calabi-Yau. An appendix is included to prove a duality theorem of the bounded derived category of quasi-finite comodules over an artinian coalgebra. | Notes: | Torrecillas, B (reprint author), Univ Almeria, Dept Algebra & Anal, E-04071 Almeria, Spain. btorreci@ual.es | Keywords: | Artin-Schelter regular algebra; Calabi-Yau algebra; Derived category; Duality; 16W30; 18E30; 18G10; 16E30 | Document URI: | http://hdl.handle.net/1942/15985 | ISSN: | 0092-7872 | e-ISSN: | 1532-4125 | DOI: | 10.1080/00927872.2012.713063 | ISI #: | 000325788500020 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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