Calabi-yau properties of down-up dg algebras

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August undefined, 2024

WebWhen the rank r(M) of M belongs to {1,2,3}, we compute H(A) case by case. The computational results in this paper give substantial support for the research of the various homological properties of such DG algebras. We find some examples, which indicate that the cohomology graded algebras of such kind of DG algebras may be not left (right ... WebDec 6, 2006 · Calabi-Yau algebras. We introduce some new algebraic structures arising naturally in the geometry of Calabi-Yau manifolds and mirror symmetry. We give a …

Pre-Calabi-Yau algebras and topological quantum field theories

WebSep 8, 2024 · Calabi-Yau properties of. -dimensional DG Sklyanin algebras. In this paper, we compute all possible differential structures of a -dimensional DG Sklyanin algebra , … WebWe describe all possible differential structures on Noetherian DG down–up algebras. For those Noetherian DG down-up algebras with nonzero differential, we compute their DG … ift short courses review

Pre-Calabi-Yau algebras and topological quantum field theories

WebSep 8, 2024 · In brief, a DG down–up algebra (Formula presented.) is a connected cochain DG algebra such that its underlying graded algebra (Formula presented.) is a graded … WebFeb 11, 2024 · In particular, Ginzburg dg algebras have the Calabi-Yau property. We show that deformed 3-Calabi-Yau completions of algebras of global dimension at most 2 are quasi-isomorphic to Ginzburg dg ... WebWhen the rank r(M) of M belongs to {1,2,3}, we compute H(A) case by case. The computational results in this paper give substantial support for the research of the … ift show 2022 dates

MR2795754 (2012j:18018) 18E30 (13F60 16E35 16E45 18E35 …

Webunder technical hypotheses on Calabi-Yau algebras Aand H, A#His Calabi-Yau if and only if the homological determinant of the H-action on Ais trivial. However, the smash product A#Hmay be Calabi-Yau even when Ais not Calabi-Yau; see, for instance, Example 1.6 below. In order to explain this phenomenon, it is natural to look into a broader class ... WebMar 27, 2024 · Recently, the constructions and studies on some specific family of connected cochain DG algebras have attracted much attention. In [5,6,7], DG down–up algebras, DG polynomial algebras and DG-free algebras are introduced and systematically studied, respectively.It is exciting to discover that non-trivial DG down–up algebras and DG free … if tsh value 3.6 from 5.6 can i conceiveWebCALABI-YAU ALGEBRAS VICTOR GINZBURG Abstract. We introduce some new algebraic structures arising naturally in the geom-etry of CY manifolds and mirror … is talent singular or plural

"WebApr 28, 2024 · In this case, the AS-regular algebra is nothing but a Calabi-Yau algebra in the sense of Ginzburg (therefore, an AS-regular algebra is also called a twisted Calabi-Yau algebra in ). Then the isomorphism ( 1 ) may be interpreted as the isomorphism between the (derived) noncommutative tangent and cotangent complexes of A , which gives rise … " - Calabi-yau properties of down-up dg algebras

Calabi-yau properties of down-up dg algebras

CALABI–YAU CONSTRUCTION BY SMOOTHING NORMAL …

WebDec 1, 2024 · In brief, a DG down–up algebra (Formula presented.) is a connected cochain DG algebra such that its underlying graded algebra (Formula presented.) is a graded … WebJan 27, 2024 · The notion of Calabi-Yau algebra is an algebraic incarnation of the notion of Calabi-Yau manifold and higher algebra -version of the notion of Frobenius algebra. …

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WebJun 29, 2024 · A (smooth) dg algebra is called (left) Calabi-Yau if (see for example here ) A! = A [ − n] Here we use the inverse dualizing complex A! = R Hom ( A e) o p ( A, A e). WebAug 14, 2024 · A celebrated result by Keller–Reiten says that 2-Calabi–Yau tilted algebras are Gorenstein and stably 3-Calabi–Yau. This note shows that the converse holds in the monomial case: a 1-Gorenstein monomial algebra and stably 3-Calabi–Yau is 2-Calabi–Yau tilted, moreover is Jacobian. We study the case of other stably Calabi–Yau …

WebMarch 14, 2024 10:19 WSPC/S0219-4988 171-JAA 1850090 Journal of Algebra and Its Applications Vol. 17, No. 5 (2024) 1850090 (45 pages) c World Scientiﬁc Publishing … WebApr 27, 2024 · Furthermore, it is proved that the DG polynomial algebra A is a Calabi-Yau DG algebra when its differential ∂ A ≠ 0 and the trivial DG polynomial algebra ( A, 0) is …

WebarXiv:math/0604596v4 [math.AG] 14 May 2007 WebJun 29, 2024 · So, are both of these definitions of Calabi-Yau compatible? Due to the work of Costello , that would be required for the above construction to actually define a TCFT, and it is often stated it actually does - however I have never actually seen …

WebFeb 11, 2024 · down-up algebras and non-trivial DG polynomial algebras are proved Calabi-Yau, respectively. CONTACT Xuefeng Mao [email protected] … ift show floorWebMay 24, 2024 · In brief, a DG down–up algebra (Formula presented.) is a connected cochain DG algebra such that its underlying graded algebra (Formula presented.) is a … ift show julyWebMay 15, 2014 · Twisted Calabi–Yau algebras are a generalisation of Ginzburg's notion of Calabi–Yau algebras. Such algebras A come equipped with a modular automorphism σ ∈ Aut (A), the case σ = id being precisely the original class of Calabi–Yau algebras. The aim of this paper is to give a concise proof of the fact that every twisted Calabi–Yau algebra … is taleo downWebThe Calabi-Yau property of cocommutative Hopf algebras is discussed by using the homological integral, a recently introduced tool for studying infinite dimensional AS … is tale of the nine tailed goodWeband Calabi-Yau property. Generally, the homological properties of a DG algebra are determined by the joint eﬀects of its underlying graded algebra structure and … ift short courseWebJul 26, 2024 · 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 it is separable modulo its graded radical and satisfies one of several suitable generalizations of the … ifts laboratoireWebMar 15, 2024 · Calabi-Yau DG algebras are introduced by Ginzburg in [9], and have a multitude of connections to representation theory, mathematical physics and non … ifts marche 2022 2023