Para-K\'ahler and pseudo-K\'ahler structures on Lie-Yamaguti algebras
| Autor: | Zhao, Jia, Feng, Yuqin, Qiao, Yu |
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| Rok vydání: | 2023 |
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| Druh dokumentu: | Working Paper |
| Popis: | For a pre-Lie-Yamaguti algebra $A$, by using its sub-adjacent Lie-Yamaguti algebra $A^c$, we are able to construct a semidirect product Lie-Yamaguti algebra via a representation of $A^c$. The investigation of such semidirect Lie-Yamaguti algebras leads us to the notions of para-K\"ahler structures and pseudo-K\"ahler structures on Lie-Yamaguti algebras, and also gives the definition of complex product structures on Lie-Yamaguti algebras which was first introduced in [25]. Furthermore, a Levi-Civita product with respect to a pseudo-Riemannian \Lie-Yamaguti algebra is introduced and we explore its relation with pre-Lie-Yamaguti algebras. Comment: arXiv admin note: text overlap with arXiv:1711.08381 by other authors |
| Databáze: | arXiv |
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