II1-SUBFACTORS ASSOCIATED WITH THE C-TENSOR CATEGORY OF A FINITE GROUP
II1-SUBFACTORS ASSOCIATED WITH THE C-TENSOR CATEGORY OF A FINITE GROUP
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与有限群的 C 张量范畴相关的 II1-子因子
DOI：
10.2140/pjm.1998.184.333
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发表时间：
1997
影响因子：
0.6
通讯作者：
R. Schaflitzel
中科院分区：
文献类型：
--
作者：
R. Schaflitzel
本文确定了具有有限指标的超定(N，N)-双模的C-⊂-张量范畴等价于给定有限群G的所有酉有限维表示的C-∗-张量范畴UG的超定II1因子R的子因子N-∗R.证明了这类子因子同构于子因子R⊂(R⊗L(C))，其中R是G的外作用α下的不动点代数，H是G的子群.ψ：H−→U(C)是H的满足一定附加条件的有限维么正射影表示，(R⊗L(Cr))H是H在R⊗L(C)上的作用下的不动点代数。
We determine the subfactors N ⊂ R of the hyperfinite II1factor R with finite index for which the C∗-tensor category of the associated (N,N)-bimodules is equivalent to the C∗-tensor category UG of all unitary finite dimensional representations of a given finite group G. It turns out that every subfactor of that kind is isomorphic to a subfactor R ⊂ (R ⊗ L(C)) , where R is the fixed point algebra under an outer action α of G, H is a subgroup of G, ψ : H −→ U(C) is a unitary finite dimensional projective representation of H satisfying a certain additional condition and (R⊗L(Cr))H is the fixed point algebra under the action α |H ⊗Adψ of H on R⊗ L(C).