Updated on 2025/04/11

写真a

 
ARANO Yuki
 
Organization
Graduate School of Mathematics Division of Mathematics Advanced Topology Associate professor
Graduate School
Graduate School of Mathematics
Undergraduate School
School of Science Department of Mathematics
Title
Associate professor
 

Papers 11

  1. Tensor category equivariant KK-theory Reviewed Open Access

    Arano, Y; Kitamura, K; Kubota, Y

    ADVANCES IN MATHEMATICS   Vol. 453   2024.9

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)   Publisher：Advances in Mathematics  

    In this paper, we introduce Kasparov's bivariant K-theory that is equivariant under symmetries of a C*-tensor category. It is motivated by some dualities in quantum group equivariant KK-theory, and the classification theory of inclusions of C*-algebras. The fundamental properties of the KK-theory, i.e., the existence of the Kasparov product, Cuntz's picture, universality, and triangulated category structure, hold in this generalization as well. Moreover, we further prove a new property specific to this theory; the invariance of KK-theory under weak Morita equivalence of the tensor categories. As an example, we study the Baum–Connes type property for 3-cocycle twists of discrete groups.

    DOI： 10.1016/j.aim.2024.109848

    Web of Science

    Scopus

  2. Ergodic theory of affine isometric actions on Hilbert spaces Reviewed International coauthorship

    Yuki Arano, Yusuke Isono, Amine Marrakchi

    Geometric and Functional Analysis   Vol. 31   page： 1013 - 1094   2021

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00039-021-00584-2

  3. Unitary spherical representations of Drinfeld doubles Reviewed Open Access

    Yuki Arano

    Journal für die reine und angewandte Mathematik   Vol. 742   page： 157 - 186   2018

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    Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1515/crelle-2015-0079

  4. Howe-Moore type theorems for quantum groups and rigid C*-tensor categories Reviewed International coauthorship

    Yuki Arano, Tim de Laat, Jonas Wahl

    Compositio Mathematica   Vol. 154 ( 2 ) page： 328 - 341   2018

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1112/S0010437X17007576

  5. Comparison of unitary duals of Drinfeld doubles and complex semisimple Lie groups Reviewed

    Yuki Arano

    Communications in Mathematical Physics   Vol. 351 ( 3 ) page： 1137 - 1147   2017

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    Authorship：Lead author,　Last author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1007/s00220-016-2704-x

  6. On the Baum--Connes conjecture for discrete quantum groups with torsion and the quantum Rosenberg Conjecture Reviewed International coauthorship

    Yuki Arano, Adam Skalski

    Proceedings of the American Mathematical Society   Vol. 149   page： 5237 - 5254   2021

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1090/proc/15598

  7. Torsion-freeness for fusion rings and tensor C*-categories Reviewed Open Access

    Yuki Arano, Kenny De Commer

    Journal of Noncommutative Geometry   Vol. 13 ( 1 ) page： 35 - 58   2019

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4171/JNCG/322

  8. A categorical perspective on the Atiyah-Segal completion theorem in KK-theory Reviewed

    Yuki Arano, Yosuke Kubota

    Journal of Noncommutative Geometry   Vol. 12 ( 2 ) page： 779 - 821   2018

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4171/JNCG/291

  9. The Fourier algebra of a rigid C*-tensor category Reviewed International coauthorship Open Access

    Yuki Arano, Tim de Laat, Jonas Wahl

    Publications of the Research Institute for Mathematical Sciences   Vol. 54 ( 2 ) page： 393 - 410   2018

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    Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.4171/PRIMS/54-2-6

  10. Compact Lie group actions with continuous Rokhlin property Reviewed Open Access

    Yuki Arano, Yosuke Kubota

    Journal of Functional Analysis   Vol. 272 ( 2 ) page： 522 - 545   2017

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (scientific journal)  

    DOI： 10.1016/j.jfa.2016.10.002

    Open Access

  11. C*-tensor categories and subfactors for totally disconnected groups Invited Reviewed International coauthorship

    Yuki Arano, Stefaan Vaes

    Operator Algebras and Applications, The Abel Symposium 2015, Springer     page： 1 - 43   2016

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    Authorship：Lead author,　Corresponding author   Language：English   Publishing type：Research paper (international conference proceedings)  

    DOI： 10.1007/978-3-319-39286-8_1

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KAKENHI (Grants-in-Aid for Scientific Research) 1

  1. 部分因子環論とテンソル圏の研究

    Grant number：24K16933  2024.4 - 2029.3

    科学研究費助成事業  若手研究

    荒野 悠輝

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    Authorship：Principal investigator 

    Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）

    作用素環の研究において，作用素環の分類は非常に重要な問題であった．このような作用素環の分類を推し進め，部分因子環論のように作用素環の包含を考えると，Galois群の類似としてテンソル圏，およびその作用素環への作用が自然にあらわれ，このテンソル圏およびその作用はもとの部分因子環を(ほぼ)決定する．
    本研究では，このようなテンソル圏およびその作用を作用素環論的視点および量子群論的な視点から研究する．特に，III0型部分因子環の分類，テンソル圏同変KKの研究，量子対称対の研究を主軸に行う．

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Teaching Experience (On-campus) 3

  1. 数学演習VI

    2024

  2. 数学演習V

    2024

  3. 複素関数論

    2024

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