Journal of Mathematical Physics, Volume 61, Issue 12, December 2020. [math]-operators (also known as relative Rota–Baxter operators) on Lie algebras have several applications in integrable systems and the classical Yang–Baxter equations. In this article, we study [math]-operators on hom-Lie algebras. We define a cochain complex for [math]-operators on hom-Lie algebras with respect to a representation. Any [math]-operator induces a hom-pre-Lie algebra structure. We express the cochain complex of an [math]-operator in terms of the specific hom-Lie algebra cochain complex. If the structure maps in a hom-Lie algebra and its representation are invertible, then we can extend the above cochain complex to a deformation complex for [math]-operators by adding the space of zero cochains. Subsequently, we study formal deformations of [math]-operators on regular hom-Lie algebras in terms of the deformation cohomology. In the end, we deduce deformations of s-Rota–Baxter operators (of weight 0) and skew-symmetric r-matrices on hom-Lie algebras as particular cases of [math]-operators on hom-Lie algebras.

## Authors

## Departments

## Libraries

## Recent Articles

- The most popular Physics Today articles of 2020
- More on doubled aspects of algebroids in double field theory
- The zilch electromagnetic conservation law revisited
- Twisted waves in symmetric and asymmetric bi-ion kappa-distributed plasmas
- Shielded radiography with gamma rays from laser-accelerated electrons in a self-trapping regime
- CSES observations of ELF wave radiation excited by the EISCAT heater
- Warm dense matter simulation via electron temperature dependent deep potential molecular dynamics
- Amplification of separated electric charge field due to the capture of laser-produced fast electrons oscillating near thin target
- Thermomagnetic instability of plasma composition gradients
- Extended source of indistinguishable polarization-entangled photons over wide angles of emission
- Extended source of indistinguishable polarization-entangled photons over wide angles of emission
- Nature journals debut open-access models
- Characterization of trap states in buried nitrogen-implanted β-Ga2O3
- Piston driven converging cylindrical shock waves in a non-ideal gas with azimuthal magnetic field
- [math]-operators on hom-Lie algebras
- The classical limit of mean-field quantum spin systems
- Effect of heating on spin-motive force induced by magnetic resonance
- 3D printing-assistant method for magneto-active pulse pump: Experiment, simulation, and deformation theory
- Electromechanical coupling and motion transduction in β-Ga2O3 vibrating channel transistors
- Flat photonics for broadband light-trapping