Rota-Baxter Leibniz Algebras and Their Constructions
In this paper, we introduce the concept of Rota-Baxter Leibniz algebras and explore two characterizations of Rota-Baxter Leibniz algebras. And we construct a number of Rota-Baxter Leibniz algebras from Leibniz algebras and associative algebras and discover some Rota-Baxter Leibniz algebras from augmented algebra, bialgebra, and weak Hopf algebra. In the end, we give all Rota-Baxter operators of weight 0 and -1 on solvable and nilpotent Leibniz algebras of dimension ≤3, respectively.
2018 ◽
Vol 28
(08)
◽
pp. 1403-1423
Keyword(s):
Keyword(s):
2010 ◽
Vol 38
(12)
◽
pp. 4613-4632
◽
Keyword(s):