Calabi-Yau algebras and the shifted noncommutative symplectic structure
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DOI: 10.1016/j.aim.2020.107126
Abstract: In this paper we show that for a Koszul Calabi-Yau algebra, there is a shifted bi-symplectic structure in the sense of Crawley-Boevey-Etingof-Ginzburg, on the cobar construction of its co-unitalized Koszul dual coalgebra, and hence its… read more here.
Keywords: calabi yau; yau algebras; symplectic structure; algebras shifted ... See more keywords
Crossed products of Calabi-Yau algebras by finite groups
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DOI: 10.1016/j.jpaa.2020.106394
Abstract: Abstract Let a finite group G act on a differential graded algebra A. This article presents necessary conditions and sufficient conditions for the skew group algebra A ⁎ G to be Calabi-Yau. In particular, when… read more here.
Keywords: calabi yau; products calabi; yau; yau algebras ... See more keywords
GRADED TWISTED CALABI–YAU ALGEBRAS ARE GENERALIZED ARTIN–SCHELTER REGULAR
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DOI: 10.1017/nmj.2020.32
Abstract: This is a general study of twisted Calabi-Yau algebras that are $\mathbb{N}$-graded and locally finite-dimensional, with the following major results. We prove that a locally finite graded algebra is twisted Calabi-Yau if and only if… read more here.
Keywords: graded twisted; calabi yau; yau algebras; twisted calabi ... See more keywords