Quantum Group Sheaf and Quantum Manifolds
| dc.creator | Volovich, I. | |
| dc.date | 1994-04-19 | |
| dc.date.accessioned | 2026-07-07T09:14:17Z | |
| dc.date.available | 2026-07-07T09:14:17Z | |
| dc.description | The 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.description | 12 pages | |
| dc.identifier | https://arxiv.org/abs/hep-th/9404110 | |
| dc.identifier | http://arxiv.org/abs/hep-th/9404110 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152617 | |
| dc.subject | High Energy Physics - Theory | |
| dc.subject | Quantum Algebra | |
| dc.title | Quantum Group Sheaf and Quantum Manifolds | |
| dc.type | text |