正规Bihom-Lie代数的上边缘算子刻画

Description of regular Bihom-Lie algebras by coboundary operators

考虑正规Bihom-Lie代数( L,[·,·],α,β)的平凡表示,给出了平凡表示对应的上边缘算子d;证明了该算子的相关性质;得到:正规Bihom-Lie代数( L,[·,·],α,β)与∧L^*上的算子d 之间存在一一对应关系。

We study trivial representation of regular Bihom-Lie algebra ( L,[·,·],α,β), and give coboundary operator d with respect to trivial representation. Then, we have some properties of coboundary operator d. Lastly, we draw a conclusion that there is an one-to-one correspondence between regular Bihom-Lie algebra ( L,[·,·],α,β) and coboundary operator d on ∧L^*.