Cohomology and deformation theory for operad with higher derivation

Xuan Yu

doi:10.1016/j.jpaa.2023.107440

Cohomology and deformation theory for operad with higher derivation

Xuan Yu

Department of Foundational Mathematics

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The purpose of this paper is to give a cohomology theory for any operad equipped with a (higher) derivation. Our construction is based on an operadic level correspondence between higher derivations and sequences of derivations and the legitimacy of this indirect approach is justified by an illustration of how the formal deformation is controlled by the cohomology. The results are generalized to the bihom-context at the end of the paper.

Original language	English
Article number	107440
Journal	Journal of Pure and Applied Algebra
Volume	227
Issue number	12
DOIs	https://doi.org/10.1016/j.jpaa.2023.107440
Publication status	Published - Dec 2023

Keywords

(higher) derivation
Cohomology
Deformation
Hom-structures

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10.1016/j.jpaa.2023.107440

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title = "Cohomology and deformation theory for operad with higher derivation",

abstract = "The purpose of this paper is to give a cohomology theory for any operad equipped with a (higher) derivation. Our construction is based on an operadic level correspondence between higher derivations and sequences of derivations and the legitimacy of this indirect approach is justified by an illustration of how the formal deformation is controlled by the cohomology. The results are generalized to the bihom-context at the end of the paper.",

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AB - The purpose of this paper is to give a cohomology theory for any operad equipped with a (higher) derivation. Our construction is based on an operadic level correspondence between higher derivations and sequences of derivations and the legitimacy of this indirect approach is justified by an illustration of how the formal deformation is controlled by the cohomology. The results are generalized to the bihom-context at the end of the paper.

KW - (higher) derivation

KW - Cohomology

KW - Deformation

KW - Hom-structures

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JO - Journal of Pure and Applied Algebra

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ER -

Cohomology and deformation theory for operad with higher derivation

Abstract

Keywords

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