Tài liệu Đề tài " Hochschild cohomology of factors with property Γ " doc

... ,x k ). Annals of Mathematics Hochschild cohomology of factors with property Γ By Erik Christensen, Florin Pop, Allan M. Sinclair, and Roger R. Smith† HOCHSCHILD COHOMOLOGY 653 Since ... product of an arbitrary type II 1 factor with a Γ- factor also has property Γ. Thus, as is well known, the McDuff factors all have property Γ, and so the resul...

Ngày tải lên: 14/02/2014, 17:20

... cannot be achieved without taking into account the needs of persons with disabilities. Moreover, persons with dis- abilities are members of societies and citizens with human rights. Of the 650 million ... cannot be achieved without taking into account the needs of persons with disabilities. Moreover, persons with dis- abilities are members of societies and citizens with...

Ngày tải lên: 13/02/2014, 15:20

... of ν H on Γ\ Σ(r)isnonzero. 5.11.7. Let us discuss the structure of  Ωinmore detail: Since Γ is of finite index in Γ  =SL(2, ) 2k we see that Γ ∩ H is of finite index in Γ  ∩ H. Furthermore Γ ... G 1 and Γ = SL(2, ) 2 . Define furthermore the subgroup Γ ∞ =  1 m 01  : m ∈  ⊂ SL(2, ), and put v γ := Im (γ )= v |cτ + d| 2 , for γ =  ab cd  , and y γ :=  0 1 ...

Ngày tải lên: 14/02/2014, 16:20

... result of Quillen [Q1]. Let π be an arbitrary group, with descending central series {Γ k } k≥1 , and associated graded Lie algebra gr ∗ Γ π := ⊕ k≥1 (Γ k /Γ k+1 ). One has a map, χ k :Γ k → I k , ... variety Γ H is either empty or a curve; i.e., each irreducible component of Γ H has dimension 1. (ii) dim(F t Γ H ) ≤ 0 and the intersection multiplicity (F t , Γ H ) is i...

Ngày tải lên: 14/02/2014, 16:20

... to the memory of Boris Moisezon Abstract We give infinite series of groups Γ and of compact complex surfaces of general type S with fundamental group Γ such that 1) Any surface S  with the same ... ψ of Π g  1 onto a free group of rank g  1 , such that in terms of the standard bases a 1 ,b 1 , a g  1 ,b g  1 , respectively γ 1 , γ g  1 ,wehave ψ(a i )=ψ(b i ) =γ...

Ngày tải lên: 14/02/2014, 16:20

... L. Lemma 2.4 (Slopes of children are far apart). The slopes of any two chil- dren of a slit with length L are separated by a distance of at least O(1/L 2+2δ ). Proof. Let w be a slit of length L.Achild ... dense G δ -subset) of P .Inparticular, P o is uncountable if P is. Proof. Since the family of residual subsets of P is closed under coun- table intersections, we assume (a...

Ngày tải lên: 14/02/2014, 17:20

... yields the claim in (2.80). This completes the proof of Lemma 6. This completes the proof of Proposition 4 and hence of Theorem 1. 3. Proof of Theorem 2 In this section we indicate how the arguments ... 2 |Z J ,N | N. 10. Next we proceed with the proof of Proposition 6(ii). Proof . Each reflection of an excursion beginning with an exit-point and ending with an entrance-point...

Ngày tải lên: 14/02/2014, 17:20

... COMPOSITION LAWS II 873 The proof of Theorem 2 not only gives a complete description of the nondegenerate orbits of the representation of Γ on Z 2 ⊗ Z 3 ⊗ Z 3 in terms of cubic rings, but also allows ... a balanced triple of ideals of S, and the three factors of SL 2 (Z) act on the bases of the ideals I 1 , I 2 , I 3 respectively. This led to a labelling of the Dynkin...

Ngày tải lên: 14/02/2014, 17:20

... (2.9), (2.13)  a∈ Z d  b∈ Z d xayb −α az −β bw −β   a∈ Z d ρ  w, {x, y, a}  γ az −β xay −α ≤  a∈ Z d wa γ az −β xay −α + ρ  w, {x, y}  γ  a∈ Z d az −β xay −α  wzxy γ + ρ  w, {x, y}  γ zxy γ ≤ 2wzxy γ . By symmetry, we ... zx γ  a∈ Z d ax −α ay −β  zx γ xy γ ≤xyz γ , where Lemma 2.10 was used in the next to last inequal...

Ngày tải lên: 14/02/2014, 17:20

... subfactors and commuting squares. It is interesting to point out that our framework of nets of subfactors as in [46] can be re- garded as a net version of the usual classification problem of subfactors ... fixed-point net of the SU(2) 1 net with the action of SU(2). That is, for each closed subgroup of SU(2), we have a fixed point net, which is an irreducible local extension of...

Ngày tải lên: 14/02/2014, 17:20