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Chen Li and
Kai Wang
Joint projective spectrum of D∞n
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| Published: |
November 22, 2024. |
| Keywords: |
joint projective spectrum; maurer-cartan form; cohomology group; self-similarity. |
| Subject [2010]: |
Primary 47A13; Secondary 20E08 and 20Cxx. |
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Abstract
In this paper, we compute the joint spectrum of D∞n with respect to the left regular representation and identify n generators of the first de Rham cohomology group of joint resolvent set, which is induced by several central linear functionals. Through action of D∞n on 2n-ary trees, we obtain a self-similar realization of the group C*-algebra of D∞n.
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| Acknowledgements
This work was supported by grants NSFC (12231005, 12026250, 11722102) and the Shanghai Technology Innovation Project (21JC1400800).
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| Author information
Chen Li
School of Mathematical Sciences
Fudan University
Shanghai, China
22110180024@m.fudan.edu.cn
Kai Wang
School of Mathematical Sciences
Fudan University
Shanghai, China
kwang@fudan.edu.cn
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