Super-bimodules and $ \mathcal{O} $-operators of Bihom-Jordan superalgebras

Ying Hou; Liangyun Chen; Keli Zheng; Ying Hou; Liangyun Chen; Keli Zheng

doi:10.3934/era.2024264

Electronic Research Archive

2024, Volume 32, Issue 10: 5717-5737. doi: 10.3934/era.2024264

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Theory article

Super-bimodules and $ \mathcal{O} $-operators of Bihom-Jordan superalgebras

1.
College of Science, Northeast Forestry University, Harbin 150040, China
2.
School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China

Received: 14 August 2024 Revised: 22 September 2024 Accepted: 09 October 2024 Published: 21 October 2024

In this paper, we mainly study super-bimodules on Bihom-Jordan superalgebras and present some interesting constructions from the perspective of super-bimodules. Meanwhile, we give abelian extension through super-bimodules. In addition, we give the representations, $ \mathcal{O} $-operators and Rota–Baxter operators of Bihom-Jordan superalgebras. Specially, using $ \mathcal{O} $-operators, we characterize Bihom-pre-Jordan superalgebras.
- Bihom-Jordan superalgebra,
- super-bimodule,
- representation,
- $ \mathcal{O} $-operator,
- Bihom-pre-Jordan superalgebra
Citation: Ying Hou, Liangyun Chen, Keli Zheng. Super-bimodules and $ \mathcal{O} $-operators of Bihom-Jordan superalgebras[J]. Electronic Research Archive, 2024, 32(10): 5717-5737. doi: 10.3934/era.2024264

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Abstract

In this paper, we mainly study super-bimodules on Bihom-Jordan superalgebras and present some interesting constructions from the perspective of super-bimodules. Meanwhile, we give abelian extension through super-bimodules. In addition, we give the representations, $ \mathcal{O} $-operators and Rota–Baxter operators of Bihom-Jordan superalgebras. Specially, using $ \mathcal{O} $-operators, we characterize Bihom-pre-Jordan superalgebras.

References

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