In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is...In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is the direct sum of two vector spaces which are also Bihom-subalgebras.Then we give four special conditions under each of which a 3-Bihom-Lie algebra has a special decomposition.Similarly,we introduce a complex structure on a 3-Bihom-Lie algebra and there are also four types of special complex structures.Finally,we establish the relation between a complex structure and a product structure.展开更多
基金Supported by NNSF of China(No.12271085 and No.12071405)supported by Sichuan Science and Technology Program(No.2023NSFSC1287).
文摘In this paper,we introduce the notion of a product structure on a 3-Bihom-Lie algebra,which is a Nijenhuis operator with some conditions.We prove that a 3-Bihom-Lie algebra has a product structure if and only if it is the direct sum of two vector spaces which are also Bihom-subalgebras.Then we give four special conditions under each of which a 3-Bihom-Lie algebra has a special decomposition.Similarly,we introduce a complex structure on a 3-Bihom-Lie algebra and there are also four types of special complex structures.Finally,we establish the relation between a complex structure and a product structure.
