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- W4287685203 abstract "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 $H=L^2(mathbb R^n, Lambda(mathbb R^n))$ 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 $Psi(A,H,D)$ generated by the Shubin type pseudodifferential operators and the elements of $A$, the zeta function ${zeta}_B(z) = {rm Tr} (B|D|^{-2z})$ 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." @default.
- W4287685203 created "2022-07-26" @default.
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- W4287685203 date "2020-08-25" @default.
- W4287685203 modified "2023-09-23" @default.
- W4287685203 title "Local Index Formulae on Noncommutative Orbifolds and Equivariant Zeta Functions for the Affine Metaplectic Group" @default.
- W4287685203 doi "https://doi.org/10.48550/arxiv.2008.11075" @default.
- W4287685203 hasPublicationYear "2020" @default.
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