一族上边缘广义李双代数的1阶上同调群和模类

The First Cohomology Groups and Modular Classes of a Family of Coboundary Generalized Lie Bialgebras

摘要: 运用三角广义李双代数胚（generalized Lie bialgebroid）及其模类（modular class）的一般理论，计算了一族上边缘广义李双代数（ \mathfraks\mathfraku\left(2\right)\times \mathbbR,\phi _0,P) 的 1 阶上同调群 H^1(\mathfraks\mathfraku\left(2\right)^\mathrm*\times \mathbbR^\mathbb*,\mathbbR) 及其模类。

Abstract: By using the general theory of triangular generalized Lie bialgebroids and their modular classes, the first cohomology groups \mathitH^1\left(\mathfraks\mathfraku\left(2\right)^\mathbf*\times \mathbbR^\mathbb*,\mathbbR\right) and modular classes of a family of coboundary generalized Lie bialgebras ( \mathfraks\mathfraku\left(2\right)\times \mathbbR,\mathit\phi _0,\mathitP) are calculated.