P Akueson and D Gurevich 1999 J. Phys. A: Math. Gen. 32 4183 doi:10.1088/0305-4470/32/23/301
Some aspects of braided geometry: differential calculus, tangent space, gauge theory
P Akueson and D Gurevich
Show affiliationsA new approach is suggested to quantum differential calculus on certain quantum varieties. It consists in replacing quantum de Rham complexes with differentials satisfying Leibniz rule by those which are in a sense close to Koszul complexes from Gurevich (1991 Leningrad Math. J. 2 801-28). We also introduce the tangent space on a quantum hyperboloid equipped with an action on the quantum function space and define the notions of quantum (pseudo)metric and quantum connection (partially defined) on it. All objects are considered from the viewpoint of flatness of quantum deformations. The problem of constructing a flatly deformed quantum gauge theory is discussed as well.
- PACS
- MSC
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17Bxx Lie algebras and Lie superalgebras (For Lie groups, see 22Exx)
81R50 Quantum groups and related algebraic methods (See also 16W35, 17B37)
- Subjects
- Dates
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Issue 23 (11 June 1999)
Received 7 October 1998
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Some aspects of braided geometry: differential calculus, tangent space, gauge theory
P Akueson and D Gurevich 1999 J. Phys. A: Math. Gen. 32 4183
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