Joint Projective Spectrum of $D_{\infty h}$

Chen Li; Kai Wang

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arXiv · 2308.09930

Joint Projective Spectrum of $D_{\infty h}$

Chen Li·Kai Wang

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Abstract

We compute the joint spectrum of $D_{\infty h}$ with respect to the left regular representation, and finds two generators of the De Rham cohomology group of joint resolvent set which is induced by different central linear functionals. Through action of $D_{\infty h}$ on 4-ary trees, we get a self-similar realization of the group $C^*$ algebra of $D_{\infty h}$.

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Chen Li, Kai Wang. 2023-08-19. Joint Projective Spectrum of $D_{\infty h}$. https://arxiv.org/abs/2308.09930

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