Product and Complex Structures on 3-Bihom-Lie Algebras  

作　　者：Juan Li Ying Hou Liangyun Chen 

机构地区：[1]School of Mathematical Sciences,Visual Computing and Virtual Reality Key Laboratory of Sichuan Province,Sichuan Normal University,Chengdu 610068,China [2]College of Science,Northeast Forestry University,Harbin 150040,China [3]School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China

出　　处：《Algebra Colloquium》2023年第4期685-700,共16页代数集刊（英文版）

基　　金：Supported by NNSF of China(No.12271085 and No.12071405);supported by Sichuan Science and Technology Program(No.2023NSFSC1287).

摘　　要：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.

关 键 词：3-Bihom-Lie algebras product structures complex structures complex product structures 

分 类 号：O15[理学—数学]