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Quantization of Semi-Classical Twists and Noncommutative Geometry

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Abstract

A problem of defining the quantum analogues for semi-classical twists in U(\(\mathfrak{g}\))[[t]] is considered. First, we study specialization at q = 1 of singular coboundary twists defined in Uq (\(\mathfrak{g}\)))[[t]] for g being a nonexceptional Lie algebra, then we consider specialization of noncoboundary twists when \(\mathfrak{g}\)=\(\mathfrak{sl}_{3}\) and obtain q-deformation of the semiclassical twist introduced by Connes and Moscovici in noncommutative geometry.

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Authors and Affiliations

  1. Theoretical Department, Institute of Physics, St. Petersburg State University, 198904, St. Petersburg, Russia

    Maxim Samsonov

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  1. Maxim Samsonov
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Correspondence to Maxim Samsonov.

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Mathematics Subject Classification: 16W30, 17B37, 81R50

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Samsonov, M. Quantization of Semi-Classical Twists and Noncommutative Geometry. Lett Math Phys 75, 63–77 (2006). https://doi.org/10.1007/s11005-005-0038-2

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  • DOI: https://doi.org/10.1007/s11005-005-0038-2

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