论文标题
非交通性轨道上的局部索引公式和仿射元组的Zeta函数
Local Index Formulae on Noncommutative Orbifolds and Equivariant Zeta Functions for the Affine Metaplectic Group
论文作者
论文摘要
我们考虑$ l^2（\ Mathbb {r}^n）$ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a $ a。代数$ a $包括所有非交易性摩ri和曲曲孔的子代数。我们用$ h = l^2（\ Mathbb r^n，λ（\ Mathbb r^n））$定义频谱三重$（a，h，d）$和欧拉操作员$ d $，这是索引$ 1 $的第一阶差异操作员。我们表明，该频谱三重具有简单的尺寸频谱：对于代数$ψ（a，h，d）中的每个操作员$ b $，由shubin型pseudoDifferential operators和$ a $ a $ a $ a $ a $ a $ a $ a $ a $ zeta函数的元素$ζ_B（z）= extriens = {\ rm tr}（\ rm d | d | $ \ mathbb c $带有最简单的杆。然后，我们的主要结果是Connes-Moscovici循环共生的明确代数表达。作为推论，我们获得了用于非交通性托里和感谢您的圆环的局部索引公式。
We consider the algebra $A$ of bounded operators on $L^2(\mathbb{R}^n)$ generated by quantizations of isometric affine canonical transformations. The algebra $A$ includes as subalgebras all noncommutative tori and toric orbifolds. We define the spectral triple $(A, H, D)$ with $H=L^2(\mathbb R^n, Λ(\mathbb R^n))$ and the Euler operator $D$, a first order differential operator of index $1$. We show that this spectral triple has simple dimension spectrum: For every operator $B$ in the algebra $Ψ(A,H,D)$ generated by the Shubin type pseudodifferential operators and the elements of $A$, the zeta function $ζ_B(z) = {\rm Tr} (B|D|^{-2z})$ has a meromorphic extension to $\mathbb C$ with at most simple poles. Our main result then is an explicit algebraic expression for the Connes-Moscovici cyclic cocycle. As a corollary we obtain local index formulae for noncommutative tori and toric orbifolds.
