Rota-Baxter Operators on pre-Lie superalgebras and beyond

Gröbner–Shirshov bases for Lie Ω-algebras and free Rota–Baxter Lie algebras

“…For example, if u = ω (3) (x 2 x 1 x 1 , x 1 , ω (1) (x 2 x 2 x 1 ))x 2 x 1 , where x 1 , x 2 ∈ X and ω (3) , ω (1) ∈ Ω, then deg(u) = 11, bre(u) = 3 and dep(u…”

“…Nijenhuis operators on Lie algebras play an important role in the study of integrability of nonlinear evolution equations [28]. Recently, there are some results on Rota-Baxter operators on Lie algebras and related topic, for example, see [1,4,5,47,49].…”

Hom-prealternative superalgebras

“…These algebras has been extended to the graded case, among which one can cite Hom-associative color algebras [29] and Hom-Lie color algebras [29], Color Hom-Poisson algebras [9], Modules over some color Hom-algebras were studied in [10] under the name of generalized Hom-algebras and also references therein. In particular, when the abelian group G giving the graduation is Z 2 the corresponding G-graded Hom-algebras are called Hom-superalgebras.Many works are done in this sense likewise Hom-Lie superalgebras, Hom-Lie admissible superalgebras [14], Rota-Baxter operator on pre-Lie superalgebras and beyond [3], The construction of Hom-Novikov superalgebras [25]. The Hom-alternative superalgebras are introduced in [1] as a Z 2 graded version of Homalternative algebras [16].…”