关于对称格上离散differential forms、图结构和多向量演算的对应原理
On a correspondence principle between discrete differential forms, graph structure and multi-vector calculus on symmetric lattices
摘要：
在\cite{DH94}的基础上，我们引入了一阶微分演算与对称格的图结构之间的双射对应关系，使得我们可以将图的互连结构完全编码在外导数中.从而得到了格的Grassmannian特征以及切空间上基本向量场之间的相互交换性。这反过来又给出了克利福德设置和由图结构赋予的自同态代数之间的一些相似之处，例如格的埃尔米特结构以及作用于格的类克利福德算子代数。这自然会导致克利福德分析的离散版本。
英文摘要：
Based on \cite{DH94}, we introduce a bijective correspondence between first order differential calculi and the graph structure of the symmetric lattice that allows one to encode completely the interconnection structure of the graph in the exterior derivative. As a result, we obtain the Grassmannian character of the lattice as well as the mutual commutativity between basic vector-fields on the tangent space. This in turn gives several similarities between the Clifford setting and the algebra of endomorphisms endowed by the graph structure, such as the hermitian structure of the lattice as well as the Clifford-like algebra of operators acting on the lattice. This naturally leads to a discrete version of Clifford Analysis.
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