Systematic study of quantum groups from the viewpoint of operator algebras

Yamanouchi对局部紧量子群在von Neumann代数上的作用作了深入的研究。他为这样的行动引入了伽罗瓦集团的概念。他成功地证明了一般局部紧量子群的可积极小作用的Galois群是对偶量子群的内蕴群。Kishimoto在非I型可分C^*-代数上对自同构群或单参数自同构群做了非常独特的研究。他证明了对于这种不具有紧算子的非零交的C^*-代数的任何不可约表示，都存在一个近似内的单参数自同构群，使得该表示相对于这个单参数自同构群是协变的。他考虑了一个量子粒子与无质量量子标量场耦合的模型，证明了该模型对于耦合常数的所有值都是基态的。Ueda对Cartan子代数上的von Neumann代数的合并自由积进行了分析。利用量子SU_q(2)的自由积型作用所产生的III型因子的不可约包含，解决了Radulescu的自由群因子具有任意指数大于4的不可约子因子这一长期存在的问题。

Yamanouchi has made an intensive study of actions of locally compact quantum groups on von Neumann algebras. He introduced a notion of a Galois group for such an action. He has succeeded in topologically identifying the Galois group of an intergrable, minimal action of a general locally compact quantum group as the intrinsic group of the dual quantum group.Kishimoto has made a very unique research on automorphisms or one-parameter automorphism groups on nontype I separable C^*-algebras. He showed that, for any irreducible representation of such a C^*-algebra without nonzero intersection with compact operators, there exists an approximately inner one-parameter automorphism group so that the representation is covariant with respect to this one-parameter automorphism group.Arai has made a progress in his research in mathematical physics. He considered a model of quantum particles coupled to a massless quantum scalar field, and showed that the model has a ground state for all values of the coupling constant.Ueda has made an anlysis on amalgamated free products of von Neumann algebras over Cartan subalgebras. By utilizing an irreducible inclusion of type III factors coming from his free-product type action of the quantum SU_q(2), he has been ble to solve the long-standing problem that the free group factor of Radulescu possesses irreducible subfactors of arbitrary index greater than 4.