Deformations and generalized derivations of Hom-Lie conformal algebras. (English) Zbl 1414.17013
Summary: The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce \(\alpha^k\)-derivations of multiplicative Hom-Lie conformal algebras and study their properties.
MSC:
| 17B56 | Cohomology of Lie (super)algebras |
| 17A42 | Other \(n\)-ary compositions \((n \ge 3)\) |
| 17B10 | Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) |
| 17B70 | Graded Lie (super)algebras |
| 16S70 | Extensions of associative rings by ideals |
Keywords:
Hom-Lie conformal algebras; \(\alpha^k\)-derivations; cohomology; deformations; generalized derivationsReferences:
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