On the hochschild cohomology of truncated cycle algebras

Bardzell, Michael; Locateli, Ana Claudia; Marcos, Eduardo N.

doi:10.1080/00927870008826917

Cited by 33 publications

(22 citation statements)

References 7 publications

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“…In case the field k is of characteristic zero, Zhang and Locateli calculated the Hochschild cohomology of truncated basic cycle algebras and truncated quiver algebras respectively [9,10,11]. For truncated basic cycle algebras over a field k of arbitrary characteristic, Bardzell, Locateli and Marcos calculated their Hochschild cohomology [12]. In this paper, we complete the calculation of the Hochschild cohomology of truncated quiver algebras over a field of arbitrary characteristic.…”

Section: Introductionmentioning

confidence: 99%

Hochschild cohomology of truncated quiver algebras

Jiang

2007

SCI CHINA SER A

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Section: Introductionmentioning

confidence: 99%

Hochschild cohomology of truncated quiver algebras

Jiang

2007

SCI CHINA SER A

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“…In Section 3, we tackle the most general situation, with different bimodules of coefficients andror more general algebras. Examples of applications are given in the two final sections, where, among other things, we apply our techniques to w x truncated algebras, recovering results obtained by Locateli 20 in characw x teristic zero; see also 1,15 . Other examples are provided by commutative monomial algebras and cancellative semigroup algebras.…”

Section: Introductionmentioning

confidence: 93%

The First Cohomology Group of an Algebra with Coefficients in a Bimodule

Cibils

Saorı́n

2001

Journal of Algebra

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“…On the other hand, the Hochschild cohomology of the (trivially graded) algebra B Γ is studied in [41,30,9]. In particular, the algebra structure of HH * (B Γ ) over a field of arbitrary characteristic was already known.…”

Section: Type Amentioning

confidence: 99%

Koszul duality patterns in Floer theory

Etgü

Lekili

2017

Geom. Topol.

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We study symplectic invariants of the open symplectic manifolds X Γ obtained by plumbing cotangent bundles of 2-spheres according to a plumbing tree Γ. For any tree Γ, we calculate (DG-)algebra models of the Fukaya category F(X Γ ) of closed exact Lagrangians in X Γ and the wrapped Fukaya category W(X Γ ). When Γ is a Dynkin tree of type A n or D n (and conjecturally also for E 6 , E 7 , E 8 ), we prove that these models for the Fukaya category F(X Γ ) and W(X Γ ) are related by (derived) Koszul duality. As an application, we give explicit computations of symplectic cohomology of X Γ for Γ = A n , D n , based on the Legendrian surgery formula of [14]. In the case that Γ is non-Dynkin, we obtain a spectral sequence that converges to symplectic cohomology whose E 2 -page is given by the Hochschild cohomology of the preprojective algebra associated to the corresponding Γ. It is conjectured that this spectral sequence is degenerate if the ground field has characteristic zero.

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On the hochschild cohomology of truncated cycle algebras

Cited by 33 publications

References 7 publications

Hochschild cohomology of truncated quiver algebras

Hochschild cohomology of truncated quiver algebras

The First Cohomology Group of an Algebra with Coefficients in a Bimodule

Koszul duality patterns in Floer theory

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