2020
DOI: 10.4310/hha.2020.v22.n1.a9
|View full text |Cite
|
Sign up to set email alerts
|

Kapranov’s construction of $\operatorname{sh}$ Leibniz algebras

Abstract: Motivated by Kapranov's discovery of an sh Lie algebra structure on the tangent complex of a Kähler manifold and Chen-Stiénon-Xu's construction of sh Leibniz algebras associated with a Lie pair, we find a general method to construct sh Leibniz algebras. Let A be a commutative dg algebra. Given a derivation of A valued in a dg module Ω, we show that there exist sh Leibniz algebra structures on the dual module of Ω. Moreover, we prove that this process establishes a functor from the category of dg module valued … Show more

Help me understand this report
View preprint versions

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
15
0

Year Published

2020
2020
2024
2024

Publication Types

Select...
4
2

Relationship

3
3

Authors

Journals

citations
Cited by 7 publications
(15 citation statements)
references
References 20 publications
0
15
0
Order By: Relevance
“…In [7], Atiyah introduced a cohomology class, which has become to be known as Atiyah class, to characterize the obstruction to the existence of holomorphic connections on a holomorphic vector bundle. The notion of Atiyah classes have been extensively developed in the past decades for diverse purposes (see [9,11,13,14,16,29,30,35]). In this section, we recall the twisted Atiyah class defined in [13] and then compute such classes in the setting of dg Loday-Pirashvili modules.…”
Section: Twisted Atiyah Classes Of Dg Loday-pirashvili Modulesmentioning
confidence: 99%
See 4 more Smart Citations
“…In [7], Atiyah introduced a cohomology class, which has become to be known as Atiyah class, to characterize the obstruction to the existence of holomorphic connections on a holomorphic vector bundle. The notion of Atiyah classes have been extensively developed in the past decades for diverse purposes (see [9,11,13,14,16,29,30,35]). In this section, we recall the twisted Atiyah class defined in [13] and then compute such classes in the setting of dg Loday-Pirashvili modules.…”
Section: Twisted Atiyah Classes Of Dg Loday-pirashvili Modulesmentioning
confidence: 99%
“…The notion of Atiyah classes have been extensively developed in the past decades for diverse purposes (see [9,11,13,14,16,29,30,35]). In this section, we recall the twisted Atiyah class defined in [13] and then compute such classes in the setting of dg Loday-Pirashvili modules.…”
Section: Twisted Atiyah Classes Of Dg Loday-pirashvili Modulesmentioning
confidence: 99%
See 3 more Smart Citations