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- Morifuji Takayuki
- Department of Mathematics, Hiyoshi Campus, Keio University
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説明
<p>A Hurwitz group is a conformal automorphism group of a compact Riemann surface with precisely 84(𝑔 − 1) automorphisms, where 𝑔 is the genus of the surface. Our starting point is a result on the smallest Hurwitz group PSL(2,𝔽7) which is the automorphism group of the Klein surface. In this paper, we generalize it to various classes of simple Hurwitz groups and discuss a relationship between the surface symmetry and spectral asymmetry for compact Riemann surfaces. To be more precise, we show that the reducibility of an element of a simple Hurwitz group is equivalent to the vanishing of the 𝜂-invariant of the corresponding mapping torus. Several wide classes of simple Hurwitz groups which include the alternating group, the Chevalley group and the Monster, which is the largest sporadic simple group, satisfy our main theorem.</p>
収録刊行物
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- Journal of the Mathematical Society of Japan
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Journal of the Mathematical Society of Japan 76 (1), 217-228, 2024
一般社団法人 日本数学会
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詳細情報 詳細情報について
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- CRID
- 1390017444754351104
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- NII書誌ID
- AA0070177X
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- ISSN
- 18811167
- 18812333
- 00255645
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- NDL書誌ID
- 033292436
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- NDL
- Crossref
- KAKEN
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- 抄録ライセンスフラグ
- 使用不可