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Representations and cohomologies of regular Hom-pre-Lie algebras.
- Source :
-
Journal of Algebra & Its Applications . Aug2020, Vol. 19 Issue 8, pN.PAG-N.PAG. 22p. - Publication Year :
- 2020
-
Abstract
- In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of regular Hom-pre-Lie algebras in terms of the cohomology theory of regular Hom-Lie algebras. As applications, we study linear deformations of regular Hom-pre-Lie algebras, which are characterized by the second cohomology groups of regular Hom-pre-Lie algebras with the coefficients in the regular representations. The notion of a Nijenhuis operator on a regular Hom-pre-Lie algebra is introduced which can generate a trivial linear deformation of a regular Hom-pre-Lie algebra. Finally, we introduce the notion of a Hessian structure on a regular Hom-pre-Lie algebra, which is a symmetric nondegenerate 2-cocycle with the coefficient in the trivial representation. We also introduce the notion of an 𝒪 -operator on a regular Hom-pre-Lie algebra, by which we give an equivalent characterization of a Hessian structure. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*COHOMOLOGY theory
*REPRESENTATIONS of algebras
*HESSIAN matrices
Subjects
Details
- Language :
- English
- ISSN :
- 02194988
- Volume :
- 19
- Issue :
- 8
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra & Its Applications
- Publication Type :
- Academic Journal
- Accession number :
- 144948788
- Full Text :
- https://doi.org/10.1142/S0219498820501492