Compatibility of quantization functors of Lie bialgebras with duality and doubling operations |
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Authors: | Benjamin Enriquez Nathan Geer |
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Institution: | (1) IRMA (CNRS) et Université de Strasbourg, 7, rue René Descartes, F-67084 Strasbourg, France;(2) Utah State University, 3900 Old Man Hill, Logan, UT 84322-3900, USA;(3) School of Mathematics, Georgia Institute of Technology, Atlanta, GA 30332-0160, USA |
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Abstract: | We study the behavior of the Etingof–Kazhdan quantization functors under the natural duality operations of Lie bialgebras
and Hopf algebras. In particular, we prove that these functors are “compatible with duality”, i.e., they commute with the
operation of duality followed by replacing the coproduct by its opposite. We then show that any quantization functor with
this property also commutes with the operation of taking doubles. As an application, we show that the Etingof–Kazhdan quantizations
of some affine Lie superalgebras coincide with their Drinfeld–Jimbo-type quantizations.
To the memory of Paulette Libermann (1919–2007) |
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Keywords: | " target="_blank"> Quantization functors dualities of Lie bialgebras Kohno– Drinfeld theorem |
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