首页|Cohomology groups of a new class of Kadison-Singer algebras
Cohomology groups of a new class of Kadison-Singer algebras
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Let N be a maximal discrete nest on an infinite-dimensional separable Hilbert space H,ξ=∑∞n=1en/2n be a separating vector for the commutant N',Eξ be the projection from H onto the subspace[Cξ]spanned by the vector ξ,and Q be the projection from K=H ⊕ H ⊕H onto the closed subspace{(η,η,η)T:η ∈H}.Suppose that L is the projection lattice generated by the projections(Eξ00000000),{(E00000000):E∈N,(I000I0000)and Q.We show that L is a Kadison-Singer lattice with the trivial commutant.Moreover,we prove that every n-th bounded cohomology group Hn(AlgL,B(K))with coefficients in B(K)is trivial for n≥1.
Kadison-Singer algebraKadison-Singer latticederivationcohomology group
Guangyu An、Xing Cheng、Jun Sheng
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School of Mathematics and Data Science,Shaanxi University of Science and Technology,Xi'an 710021,China
国家自然科学基金陕西省自然科学基金Shaanxi College Students Innovation and Entrepreneurship Training Program
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