Đề tài " On deformations of associative algebras " potx

... ) Annals of Mathematics On deformations of associative algebras By Roman Bezrukavnikov and Victor Ginzburg* Annals of Mathematics, 166 (2007), 533–548 On deformations of associative algebras By ... a-bimodule extensions of a by J/J 2 . The class of the extension in (1.1.4) may be viewed as a noncommutative version of Kodaira-Spencer class. ON DEFOR...

Ngày tải lên: 15/03/2014, 09:20

... 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 given in Section 2 for the Wiener ... −e −cκ a φ 2 ) 2 . (2.34) This completes the proof of Proposition 2. ON THE VOLUME OF THE INTERSECTION OF TWO WIENER SAUSAGES 755 2.2. The lower bound in Theorem 1. In this se...

Ngày tải lên: 14/02/2014, 17:20

... measure for the size of the neighbourhood V of the singular set on noncontracted components is the diameter of ϕ(V )inM; on contracted components one may take the smallest ε with V contained in the ... claim on pseudo-holomorphic sections of M [d] \ H d LEFSCHETZ FIBRATIONS 975 is clear from the definition of J M [d] in Proposition 2.2 and the description of β in Lemma 1.6. H...

Ngày tải lên: 16/02/2014, 05:20

... two components of type (ii) meeting along a conic, or (c) X consists of ν,3 ν  r, components of type (ii) meeting along lines and the dual graph G D of a general hyperplane section D of X is ... union of planes. As a first application of this approach, we shall see that there are strong constraints on the invariants of a smooth projective surface which degener- ates to confi...

Ngày tải lên: 16/02/2014, 06:20

... quantita- tive version is established (in the sense that one bounds explicitly the number of exceptional subspaces). We now turn to the proof of Theorem 5. Keep the notation and the assumptions of this theorem. ... every element of Q(β) ∩(0, 1) has an eventually periodic β-expansion. 5. Proofs of Theorems 1 to 4 We begin by a short proof of Theorem 2. Proof of Theorem 2. Let a =...

Ngày tải lên: 16/02/2014, 06:20

... that ON THE CLASSIFICATION PROBLEM FOR NUCLEAR C ∗ -ALGEBRAS 1043 the moment one relaxes the slow dimension growth condition for AH algebras (and therefore, a fortiori for ASH algebras) , one obtains ... C ∗ -algebras satisfying the Universal Coefficient Theorem, the Elliott-Gong-Li classification of simple unital AH algebras of very slow dimension growth, and Lin’s classification...

Ngày tải lên: 16/02/2014, 06:20

... convex hull of ˜ R u is equal to the closed convex hull of R u (see e.g. [5, Lemma 2.12]). The proofs in [12] and [8] of existence of points of Fr´echet differentiability of Lipschitz functions ... point of a surface then a suitable small local deformation of the surface causes a nonsmall perturbation of the function t → D f (γ(t)). Here we perform a finite number of such lo...

Ngày tải lên: 05/03/2014, 23:20

... (“co-type”) case of inclusions of von Neumann algebras, by using a similar strategy to the way the notions of amenabilty and property (T) were extended from single algebras to inclusions of algebras ... group of M is trivial. This solves a long standing problem of R. V. Kadison. Also, our results bring some insight into a recent problem of A. Connes and answer a number of...

Ngày tải lên: 06/03/2014, 08:21

... this proof of Corollary 2 is nonconstructive as well. Here we give another, constructive proof of this corollary. Combined with our proof of The- orem 2, it yields a constructive realization of G ... admit constructive description of genera- tors of the field of rational G-invariant functions). However for Corollary 2 of Theorem 1 we are able to give another, constructive proof...

Ngày tải lên: 14/03/2014, 22:20

... its parent. By definition, D is said to be of generation 0. Any child of D is of gen- eration 1. In general, a drop is of generation k if and only if its parent is of generation k − 1. Given a point ... argument. This is one of the reasons why we adopt the original construction of [P2] in what follows. Here is the strategy of this construction: For the above simple choice of...

Ngày tải lên: 14/03/2014, 22:20