Constructions and representations on BiHom-$ \delta $-Jordan Lie color algebras

Jiaqi Li; Hongrui Yu; Lili Ma; Jiaqi Li; Hongrui Yu; Lili Ma

doi:10.3934/math.2026813

AIMS Mathematics

2026, Volume 11, Issue 7: 20029-20049. doi: 10.3934/math.2026813

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Research article

Constructions and representations on BiHom-$ \delta $-Jordan Lie color algebras

1.
College of Science, Minzu University of China, Beijing 100081, China
2.
College of Science, Hebei Normal University, Shijiazhuang 050024, China
3.
College of Science, Qiqihar University, Qiqihar 161006, China
4.
College of Science, Shenyang Aerospace University, Shenyang 110136, China

Received: 31 December 2025 Revised: 28 May 2026 Accepted: 10 June 2026 Published: 08 July 2026
MSC : 17A99, 17B40, 17B56

The aim of this paper is to study BiHom-$ \delta $-Jordan Lie color algebras. Three kinds of BiHom-$ \delta $-Jordan Lie color algebras are constructed using suitable bilinear operators, respectively. Then representations and cohomologies are given to show some properties on BiHom-$ \delta $-Jordan Lie color algebras. Moreover, trivial representations and adjoint representations on BiHom-$ \delta $-Jordan Lie color algebras are discussed.
- BiHom-$ \delta $-Jordan Lie color algebra,
- representation,
- trivial representation,
- adjoint representation,
- derivation
Citation: Jiaqi Li, Hongrui Yu, Lili Ma. Constructions and representations on BiHom-$ \delta $-Jordan Lie color algebras[J]. AIMS Mathematics, 2026, 11(7): 20029-20049. doi: 10.3934/math.2026813

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Abstract

The aim of this paper is to study BiHom-$ \delta $-Jordan Lie color algebras. Three kinds of BiHom-$ \delta $-Jordan Lie color algebras are constructed using suitable bilinear operators, respectively. Then representations and cohomologies are given to show some properties on BiHom-$ \delta $-Jordan Lie color algebras. Moreover, trivial representations and adjoint representations on BiHom-$ \delta $-Jordan Lie color algebras are discussed.

References

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