Abstract
In this paper, we first introduce the notion of BiHom–Lie superalgebras, which is a generalization of both BiHom–Lie algebras and Hom–Lie superalgebras. Also, we explore some general classes of BiHom–Lie admissible superalgebras and describe all these classes via G-BiHom-associative superalgebras, where G is a subgroup of the symmetric group \(S_{3}\). Finally, we obtain a method to construct the solutions of the BiHom–Yang–Baxter equation from BiHom–Lie superalgebras.
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Acknowledgements
The authors are grateful to the referees for carefully reading the manuscript and for many valuable comments which largely improved the article. The work of S. Wang is supported by the Anhui Provincial Natural Science Foundation (Nos. 1908085MA03 and 1808085MA14) and the outstanding top-notch talent cultivation project of Anhui Province (No. gxfx2017123). The work of S. Guo is supported by the NSF of China (No. 11761017) and Guizhou Provincial Science and Technology Foundation (No. [2020]1Y005).
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Wang, S., Guo, S. BiHom–Lie Superalgebra Structures and BiHom–Yang–Baxter Equations. Adv. Appl. Clifford Algebras 30, 35 (2020). https://doi.org/10.1007/s00006-020-01060-0
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DOI: https://doi.org/10.1007/s00006-020-01060-0