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6J Symbols Duality Relations

Abstract : It is known that the Fourier transformation of the square of (6j) symbols has a simple expression in the case of su(2) and U_q(su(2)) when q is a root of unit. The aim of the present work is to unravel the algebraic structure behind these identities. We show that the double crossproduct construction H_1\bowtie H_2 of two Hopf algebras and the bicrossproduct construction H_2^{*}\lrbicross H_1 are the Hopf algebras structures behind these identities by analysing different examples. We study the case where D= H_1\bowtie H_2 is equal to the group algebra of ISU(2), SL(2,C) and where D is a quantum double of a finite group, of SU(2) and of U_q(su(2)) when q is real.
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http://hal.in2p3.fr/in2p3-00182564
Contributor : Francoise Duceau <>
Submitted on : Friday, October 26, 2007 - 2:17:20 PM
Last modification on : Thursday, November 26, 2020 - 12:54:02 PM

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K. Noui, P. Roche, L. Freidel. 6J Symbols Duality Relations. Journal of Mathematical Physics, American Institute of Physics (AIP), 2007, 48/11, pp.113512. ⟨10.1063/1.2803507⟩. ⟨in2p3-00182564⟩

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