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応用数理研究部門(小澤 登高)
Showing the original Japanese · View translation
作用素環の解析的な手法で、離散群を研究する研究室。

AboutAbout the lab
群の対称性を、作用素環で解析する。
小澤研究室は、
群は
群の
伝統的な
Key terms
- 作用素環
- 線形
空間の 上の 作用素が 生成する 代数系を、 位相で 完備化した もの。 C*環と von Neumann環が ある - 離散群
- とびとびの
要素から なる群。 結晶の 対称性のように、 ものの 対称性を 記述する - Kazhdanの
性質(T) - ほぼ不変な
ベクトルを もつ表現は 本当に 不変な ベクトルを もつ、と いう 群の 硬さの 性質
ResearchResearch themes
作用素環と
*Illustrative image作用素環と離散群の関わり
数理物理や
*Illustrative image解析学的群論
Kazhdanの
*Illustrative image粗幾何学とvon Neumann環の問題
擬局所的作用素が
MembersFaculty
- Professor小澤 登高
VoicesStudent voices
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Cayley graph of Alternating Group A5” Kathryn Cramer / CC BY-SA 4.0 (cropped)
- 作用素環と
離散群の 関わり: “Kelli graph free prod” Tosha / Public domain (cropped) - 解析学的群論: “Dutch national supercomputer "Huygens"” Dennis van Zuijlekom / CC BY-SA 2.0 (cropped)
- 粗幾何学と
von Neumann環の 問題: “Hyperbolic 3d order 4 hexagonal tiling” Claudio Rocchini / CC BY-SA 3.0 (cropped) - Related lab (応用数理研究部門
(磯野 優介) ): “Bernoullishift” Andreas Mandl / CC BY-SA 3.0 (cropped) - Related lab (応用数理研究部門
(SEHNEM, Camila) ): “Hyperbolic tiling 7 7-2” Double sharp (talk), based on this picture by Jim McNeill, but with the remaining overlapping heptagons left as outlines instead of deleted. A green background to the tiling has also been added. Created using Tyler and Paint. / Public domain (cropped) - Related lab (応用数理研究部門
(岸本 展) ): “Rogue waves breaking behavior at different crossing angles, McAllister 2019” McAllister et al 2019 / CC BY 4.0 (cropped) - Related lab (応用数理研究部門
(牧野 和久) ): “B functies 2var versie02” Bob.v.R / CC BY-SA 4.0 (cropped)
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