Quantum Group Sheaf and Quantum Manifolds

dc.creatorVolovich, I.
dc.date1994-04-19
dc.date.accessioned2026-07-07T09:14:17Z
dc.date.available2026-07-07T09:14:17Z
dc.descriptionThe problem of introducing a dependence of elements of quantum group on classical parameters is considered. It is suggested to interpret a homomorphism from the algebra of functions on quantum group to the algebra of sections of a sheaf of algebras on a classical manifold as describing such a dependence. It is argued that the functorial point of view of group schemes is more appropriate in quantum group field theory. A sheaf of the Hopf algebras over the manifold (quantum sheaf) is constructed by using bosonization formulas for the algebra of functions on the quantum group $SU_{q}(2)$ and the theory of repre- sentations of canonical commutation relations. A family of automorphisms of the Hopf algebra depending on classical variables is described. Quantum manifolds, i.e. manifolds with commutative and non-commutative coordinates are discussed as a generalization of supermanifolds. Quantum group chiral fields and relations with algebraic differential calculus are discussed.
dc.description12 pages
dc.identifierhttps://arxiv.org/abs/hep-th/9404110
dc.identifierhttp://arxiv.org/abs/hep-th/9404110
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152617
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleQuantum Group Sheaf and Quantum Manifolds
dc.typetext

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