共形变形非对易环面II的局部不变量：多重算子积分
Local invariants of conformally deformed non-commutative tori II: multiple operator integrals
摘要：
我们明确地计算局部不变量（热核系数）的共形变形的非交换$d$ -环面使用多个算子积分。我们推导出一个递归公式，可以很容易地产生一个明确的表达任何顺序$k$和任何尺寸$d$的局部不变量。我们的递归公式可以方便地产生与模算子有关的所有公式，这些公式以前是在$d\in\{2,4\}$和$k\in\{0,2,4\}$的增量步骤中获得的。我们通过在模算子中写下一些已知的（$k=2$，$d=2$）和一些新的（$k=2$，$d\geq 3$）公式来证明这一点。
英文摘要：
We explicitly compute the local invariants (heat kernel coefficients) of a conformally deformed non-commutative $d$-torus using multiple operator integrals. We derive a recursive formula that easily produces an explicit expression for the local invariants of any order $k$ and in any dimension $d$. Our recursive formula can conveniently produce all formulas related to the modular operator, which before were obtained in incremental steps for $d\in\{2,4\}$ and $k\in\{0,2,4\}$. We exemplify this by writing down some known ($k=2$, $d=2$) and some novel ($k=2$, $d\geq 3$) formulas in the modular operator.
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