论文标题
通电复合物的绿色功能
Green functions of Energized complexes
论文作者
论文摘要
如果H是在简单复合物G上的环值函数，则可以定义两个矩阵L和G，其中矩阵条目是同型相交的H能量。我们知道，G上所有H值的总和等于绿色矩阵条目G（x，y）的总和。我们还已经看到，L或G的决定因素既是H（x）的乘积。在h（x）是维度的均衡的情况下，能量值的总和是标准的欧拉特征，而行列式为单位。如果h（x）是环中的单位，则l，g是彼此的同一光谱和反矩阵的积分二次形式。我们在这里证明，相交集的所有对H（x）^* h（y）上的二次能量表达式是绿色函数条目的符号和正方形的总和。在h是尺寸奇迹的情况下，二次能量表达是WU的特征。对于一般h，二次能量表达类似于伊森伯格型相互作用。如果h在标准环或操作员代数中的单一操作员组中采用单位值，则g的偶联物是L的倒数。
If h is a ring-valued function on a simplicial complex G we can define two matrices L and g, where the matrix entries are the h energy of homoclinic intersections. We know that the sum over all h values on G is equal to the sum of the Green matrix entries g(x,y). We also have already seen that that the determinants of L or g are both the product of the h(x). In the case where h(x) is the parity of dimension, the sum of the energy values was the standard Euler characteristic and the determinant was a unit. If h(x) was the unit in the ring then L,g are integral quadratic forms which are isospectral and inverse matrices of each other. We prove here that the quadratic energy expression summing over all pairs h(x)^* h(y) of intersecting sets is a signed sum of squares of Green function entries. The quadratic energy expression is Wu characteristic in the case when h is dimension parity. For general h, the quadratic energy expression resembles an Ising Heisenberg type interaction. The conjugate of g is the inverse of L if h takes unit values in a normed ring or in the group of unitary operators in an operator algebra.
