Color hom-Lie algebras, color hom-Leibniz algebras and color omni-hom-Lie algebras. (English) Zbl 1537.17031
Silvestrov, Sergei (ed.) et al., Non-commutative and non-associative algebra and analysis structures. SPAS 2019. Selected papers based on the presentations at the international conference on stochastic processes and algebraic structures – from theory towards applications, Västerås, Sweden, September 30 – October 2, 2019. Cham: Springer. Springer Proc. Math. Stat. 426, 61-79 (2023).
Summary: In this paper, the representations of color hom-Lie algebras have been reviewed and the existence of a series of coboundary operators is demonstrated. Moreover, the notion of a color omni-hom-Lie algebra associated to a linear space and an even invertible linear map have been introduced. In addition, characterization method for regular color hom-Lie algebra structures on a linear space is examined and it is shown that the underlying algebraic structure of the color omni-hom-Lie algebra is a color hom-Leibniz a algebra.
For the entire collection see [Zbl 1531.17004].
For the entire collection see [Zbl 1531.17004].
MSC:
| 17B61 | Hom-Lie and related algebras |
| 17D30 | (non-Lie) Hom algebras and topics |
| 17B75 | Color Lie (super)algebras |
| 17A32 | Leibniz algebras |
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