On compatible Hom-Lie triple systems. (English) Zbl 07913037
Summary: In this paper, we consider compatible Hom-Lie triple systems. More precisely, compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie triple systems. As applications of cohomology, we study linear deformations and abelian extensions of compatible Hom-Lie triple systems.
MSC:
| 13D10 | Deformations and infinitesimal methods in commutative ring theory |
| 17A40 | Ternary compositions |
| 17B56 | Cohomology of Lie (super)algebras |
| 17B61 | Hom-Lie and related algebras |
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