2021
DOI: 10.48550/arxiv.2107.09259
|View full text |Cite
Preprint
|
Sign up to set email alerts
|

(Co)homology of compatible associative algebras

Abstract: In this paper, we define and study (co)homology theories of a compatible associative algebra A. At first, we construct a new graded Lie algebra whose Maurer-Cartan elements are given by compatible associative structures. Then we define the cohomology of a compatible associative algebra A and as applications, we study extensions, deformations and extensibility of finite order deformations of A. We end this paper by considering compatible presimplicial vector spaces and the homology of compatible associative alg… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
2
1

Citation Types

0
9
0

Year Published

2021
2021
2023
2023

Publication Types

Select...
4

Relationship

3
1

Authors

Journals

citations
Cited by 4 publications
(9 citation statements)
references
References 19 publications
0
9
0
Order By: Relevance
“…Here δ π1 and δ π2 denote the Hochschild coboundary operators for the associative algebras (A, • 1 ) and (A, • 2 ), respectively. This is the cochain complex for the cohomology of the compatible associative algebra (A, • 1 , • 2 ) considered in [7]. As a conclusion, the cohomology of the compatible associative algebra (A, • 1 , • 2 ) inherits a Gerstenhaber structure.…”
Section: Theorem the Triplementioning
confidence: 79%
See 3 more Smart Citations
“…Here δ π1 and δ π2 denote the Hochschild coboundary operators for the associative algebras (A, • 1 ) and (A, • 2 ), respectively. This is the cochain complex for the cohomology of the compatible associative algebra (A, • 1 , • 2 ) considered in [7]. As a conclusion, the cohomology of the compatible associative algebra (A, • 1 , • 2 ) inherits a Gerstenhaber structure.…”
Section: Theorem the Triplementioning
confidence: 79%
“…Given a compatible multiplication (π 1 , π 2 ) on O, we define the cohomology induced by (π 1 , π 2 ) as the cohomology induced by the corresponding multiplication on the operad O comp . When O is the endomorphism operad End A and compatible multiplication (π 1 , π 2 ) corresponds to the compatible associative algebra (A, • 1 , • 2 ), we obtain the cohomology of the compatible associative algebra introduced in [7]. As a consequence of our study, we obtain a Gerstenhaber algebra structure on the cohomology of any compatible associative algebra.…”
Section: Compatible Loday-algebrasmentioning
confidence: 85%
See 2 more Smart Citations
“…Similarly, compatible associative algebras and their relations with associative Yang-Baxter equations, quiver representations and bialgebra theory are explored in [20,23,24,32]. Recently, compatible Lie algebras and compatible associative algebras are studied in [4,15] from cohomological points of view. In the geometric context, compatible Poisson structures were appeared in the mathematical study of biHamiltonian mechanics [13,19].…”
Section: Introductionmentioning
confidence: 99%