Automorphisms on generalized Cuntz algebra and quasi free state

从一个可调节离散组G进入（M）的同源现象是调用G内核。Then G-kernels α， β are outer conjugate if there is an automorphism θ of M with α[θ] = [θ]β。我们的目标完全是对G内核的混淆。If G×R acts on commutative von Neumann algebra C， R is ergodic and Q=G/N， then we at first characterize an invariant H-D4-D13-D1（Q × R，C）in algebraic way in terms of H-D13-D1（Q × R，C），H-D13-D1（Q，C）-D1×Z-D1（Q，H I D11 E D1（R，C））， and we obtain two exact sequences.We consider generalized Cantz algebra induced by B-Hilbert bimoduleX of finite type。我们展示了固定的点代数，并尊重欺骗动作很简单，如果B是X-典型。B的定义是X-平均数，即过渡矩阵是平均数的通用化。让你在X上做个操作员。If a certain automorphism，D2U，D2 on generalized Cantz algebra is inner， then it is trivial on a relative commutant of the fixed point algebra。将此应用于Cuntz-Krieger代数， the automorphisms--D2 U--D2是inner or weakly inner with canonical state ψ if and only if the operator U是一种coboundary类型，我们展示我们给一个群体一个tensor product formulae of characteristic invariant for actions of an group。在III型的某些因素的情况下，我们可以计算公式。让α，β，做两个相互交流的动作。We give a formulae to give？teristic invariant for an extManagement action（在partial crossed product by？）在这种情况下，我们可以清楚地显示出一种典型的III型因子，因为该组是阿拉伯裔。

A homomorphism α from an amenable discrete group G into Out(M)is call G-kernel. Then G-kernels α, β are outer conjugate if there is an automorphism θ of M with α[θ] = [θ]β. Our aim is to classify completely the conjugacy of G-kernel. If G×R acts on commutative von Neumann algebra C, R is ergodic and Q=G/N, then we at first characterize an invariant HィイD4〜ィエD4ィイD13ィエD1(Q×R,C)in algebraic way in terms of HィイD13ィエD1(Q×R,C), HィイD13ィエD1(Q,C)ィイD1RィエD1×ZィイD12ィエD1(Q,HィイD11ィエD1(R,C)), and we obtain two exact sequences.We consider generalized Cuntz algebra induced by B-Hilbert bimoduleX of finite type. We show that the fixed point algebra with respect to gauge action is simple if and only if B is X-aperiodic. The definition of B is X-aperidodic is a generalization that transition matrix is aperiodic. Let U be an operator on X. If a certain automorphism αィイD2UィエD2 on generalized Cuntz algebra is inner, then it is trivial on a relative commutant of the fixed point algebra. Applying this to Cuntz-Krieger algebra, the automorphisms αィイD2UィエD2 is inner or weakly inner with canonical state ψ if and only if the operator U is a type of coboundary.And we show that we give a tensor product formulae of characteristic invariant for actions of an group. In the case of a certain factor of type III, we can compute explicitly the formulae. Let α,β be two actions which commute mutually. We give a formulae to give characteristic invariant for an extended action α on the partial crossed product by β. we can show explicitly the formulae for a certain factor of type III in the case that the group is abelian,