2006/04/25 by L. Freidel, K. Noui, P. Roche +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Combinatorial Mathematics #Algebra over a field #Algebraic number #Algebraic structure #Algebraic structures and combinatorial models #Crossed product #Duality (order theory) #Finite Group Theory Research #Group (periodic table) #Hopf algebra #Product (mathematics) #Quantum group #Simple (philosophy) #hep-th
paper · pdf · doi:10.1063/1.2803507
published as J.Math.Phys.48:113512,2007 · 28 pages, 2 figures
arxiv created 2006/04/25 · openalex publication_date 2007/11/01 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is known that the Fourier transformation of the square of (6j) symbols has a simple expression in the case of su(2) and Uq(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 cross product construction H1⋈H2 of two Hopf algebras and the bi-cross-product construction H2*⧑H1 are the Hopf algebra structures behind these identities by analyzing different examples. We study the case where D=H1⋈H2 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 Uq(su(2)) when q is real.