Linear connections in non-commutative geometry
Linear connections in non-commutative geometry
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非交换几何中的线性连接
DOI：
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发表时间：
1994
期刊：
影响因子：
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通讯作者：
J. Mourad
中科院分区：
文献类型：
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作者：
J. Mourad
给出了非交换代数上线性联络的一个构造。该构造依赖于交换几何的莱布尼茨规则的推广，并使用的双模结构。的两个副本的置换的非交换几何的框架的扩展发挥了特殊的作用。首先在基于微分学的Dubois Violette的基础上给出了线性联络的构造以及挠率和曲率的定义，然后给出了基于Dirac算子的Connes微分学和其他微分学的一般形式.得到的协变导数容许的几个副本的张量积的扩展。这些结构的例子说明了代数的矩阵。
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalization of the Leibniz rules of commutative geometry and uses the bimodule structure of . A special role is played by the extension to the framework of non-commutative geometry of the permutation of two copies of . The construction of the linear connection as well as the definition of torsion and curvature is first proposed in the setting of the derivations based differential calculus of Dubois-Violette and then a general of the Dirac operator based differential calculus of Connes and other differential calculuses is given. The covariant derivative obtained admits an extension to the tensor product of several copies of . These constructions are illustrated with the example of the algebra of matrices.