$(m, n)$-Hom-Lie algebras

Matching BiHom-Rota-Baxter Algebras and Related Structures

“…The Hom-Lie algebra was introduced by Hartwig, Larsson and Silvestrov [1]. Further research on Hom-Lie algebras could be found in [2][3][4][5][6][7] and references cited therein. As a generalization of Hom-Lie algebra, Graziani etc.…”

Matching Hom-Setting of Rota-Baxter Algebras, Dendriform Algebras, and Pre-Lie Algebras

“…Recently, there have been several interesting developments of Hom-Lie algebras in mathematics and mathematical physics, including Hom-Lie bialgebras [2,3], quadratic Hom-Lie algebras [4], involutive Hom-semigroups [5], deformed vector fields and differential calculus [6], representations [7,8], cohomology and homology theory [9,10], Yetter-Drinfeld categories [11], Hom-Yang-Baxter equations [12][13][14][15][16], Hom-Lie 2-algebras [17,18], ðm, nÞ-Hom-Lie alge-bras [19], Hom-left-symmetric algebras [20], and enveloping algebras [21]. In particular, the Hom-Lie algebra on semisimple Lie algebras was studied in [22], and the Hom-Lie structure on affine Kac-Moody was constructed in [23].…”

Matching Hom-Setting of Rota-Baxter algebras, dendriform algebras and pre-Lie algebras

“…Recently, there have been several interesting developments of Hom-Lie algebras in mathematics and mathematics physics, including Hom-Lie bialgebras [9,12], quadratic Hom-Lie algebras [7], involutive Hom-semigroups [49], deformed vector fields and differential calculus [26], representations [39,48], cohomology and homology theory [3,45], Yetter-Drinfeld categories [43], Hom-Yang-Baxter equations [10,11,41,47], Hom-Lie 2-algebras [40,42], (m, n)-Hom-Lie algebras [32], Hom-left-symmetric algebras [34] and enveloping algebras [20]. In particular, the Hom-Lie algebra on semisimple Lie algebras was studied in [25] and the Hom-Lie structure on affine Kac-Moody was constructed in [37].…”