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• W2082029985 abstract "A one parameter quantum deformationS μ L(2,ℂ) ofSL(2,ℂ) is introduced and investigated. An analog of the Iwasawa decomposition is proved. The compact part of this decomposition coincides withS μ U(2), whereas the solvable part is identified as a Pontryagin dual ofS μ U(2). It shows thatS μ L(2,ℂ) is the result of the dual version of Drinfeld's double group construction applied toS μ U(2). The same construction applied to any compact quantum groupG c is discussed in detail. In particular the explicit formulae for the Haar measures on the Pontryagin dualG d ofG c and on the double groupG are given. We show that there exists remarkable 1-1 correspondence between representations ofG and bicovariant bimodules (“tensor bundles”) overG c . The theory of smooth representations ofS μ L(2,ℂ) is the same as that ofSL(2,ℂ) (Clebsh-Gordon coefficients are however modified). The corresponding “tame” bicovariant bimodules onS μ U(2) are classified. An application to 4D + differential calculus is presented. The nonsmooth case is also discussed." @default.
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• W2082029985 date "1990-06-01" @default.
• W2082029985 modified "2023-10-14" @default.
• W2082029985 title "Quantum deformation of lorentz group" @default.
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• W2082029985 doi "https://doi.org/10.1007/bf02473358" @default.
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