Noncommutative finite dimensional manifo
➤ Gửi thông báo lỗi ⚠️ Báo cáo tài liệu vi phạmNội dung chi tiết: Noncommutative finite dimensional manifo
Noncommutative finite dimensional manifo
Conmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative Fin Noncommutative finite dimensional manifo nite Dimensional Manifolds II: Moduli Space and Structure of Noiiconimutative 3-SpheresAlain Connes1,2 \ Michel Dubois-Violette41 College de France. 3, rue d'Ulm. Paris. F-75005 France. E-mail: alain@connes.orgI.H.E.S.. 35. route deChartres. F-91440 Bures-sur-Yuette. FranceMathematics Department. Va Noncommutative finite dimensional manifo nderbilt University. Nashville. TN 37235. USA4 Laboratoirc de Physique Thcoriquc, UMR 8627. Univcrsitc Paris XL Bailment 210,F-91 405 Orsay Codex, FraNoncommutative finite dimensional manifo
nce. E-mail: Michel.Dubois-Violcttc@ th.u-psud.irReceived: 31 July 2006 / Accepted: 20 November 2007Published online: 6 May 2008 - Ỡ Springer-Verlag 2Conmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative Fin Noncommutative finite dimensional manifo on of central quadratic form for quadratic algebras, and a general theory which creates a bridge between non-commutative differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic algebra to a c*-algebra constructed from the characteris Noncommutative finite dimensional manifo tic variety and the hermitian line bundle associated to the central quadratic form. We apply the general theory in the case of noncommutative 3-sphereNoncommutative finite dimensional manifo
s and show that the above morphism corresponds to a natural ramified covering by a non-commutative 3-dimensional nilmanifold. We then compute the JacoConmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative Fin Noncommutative finite dimensional manifo and complex moduli spaces of noncommutative 3-spheres. relate the real one to root systems and the complex one to the orbits of a birational cubic automorphism of three dimensional projective space. We classify the algebras and establish duality relations between them.Contents1Introduction ......... Noncommutative finite dimensional manifo ............................................... 252The Noncommutative 3-Spheres S3(A) c R4(A) .......................... 272.1Unitary “up to scale"...Noncommutative finite dimensional manifo
........................................ 272.2Equation ch 1/2(Ơ) = 0 ......................................... 272.3Noncommutative 3-spheres and 4-plaConmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative Fin Noncommutative finite dimensional manifo ....................... 323.2Trigonometric parameters (p of s3............................... 343.3. VI in terms of Dy ............................................ 353.4Roots A = /?(G.T)............................................... 373.5Singular hyperplanes Ha,n.................................... Noncommutative finite dimensional manifo ... 3724A. Conncs, M. Dubois-Violette3.6Kernel of the exponential map: r(T) (nodal group of T)................... 373.7Group of nodal vectors/V(G. T)Noncommutative finite dimensional manifo
c T(T).................................... 373.8Affine Weyl group Wfl.................................................... 383.9Affine Weyl group W''..Conmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative Fin Noncommutative finite dimensional manifo .............................................................. 404.1Compatibility of F with the triangulation by alcoves......................414.2Invariance of R* under the flow F........................................ 425The Geometric Data of Rj.................................................... Noncommutative finite dimensional manifo ... 46Conmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative FinConmiun. Math. Phys. 281,23-127 (2008)Digital Object Identifier (DOI) 10.1007/s00220-008-0472-yCommunications inMathematical PhysicsNoncommutative FinGọi ngay
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