Non commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres

Simple item page
dc.creatorConnes, Alain
dc.creatorDubois-Violette, Michel
dc.date2005-11-14
dc.date.accessioned2026-07-07T06:51:12Z
dc.date.available2026-07-07T06:51:12Z
dc.descriptionThis paper contains detailed proofs of our results on the moduli space and the structure of noncommutative 3-spheres. We develop the notion of central quadratic form for quadratic algebras, and a general theory which creates a bridge between noncommutative differential geometry and its purely algebraic counterpart. It allows to construct a morphism from an involutive quadratic algebras to a C*-algebra constructed from the characteristic variety and the hermitian line bundle associated to the central quadratic form. We apply the general theory in the case of noncommutative 3-spheres and show that the above morphism corresponds to a natural ramified covering by a noncommutative 3-dimensional nilmanifold. We then compute the Jacobian of the ramified covering and obtain the answer as the product of a period (of an elliptic integral) by a rational function. We describe the real 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.
dc.description96 pages
dc.identifierhttps://arxiv.org/abs/math/0511337
dc.identifierhttp://arxiv.org/abs/math/0511337
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/104909
dc.subjectQuantum Algebra
dc.subjectGeneral Relativity and Quantum Cosmology
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectRings and Algebras
dc.titleNon commutative finite dimensional manifolds II. Moduli space and structure of non commutative 3-spheres
dc.typetext

Files

Collections

arXiv