6J Symbols Duality Relations
高能物理 - 理论
2008-11-26 v1
摘要
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.
引用
@article{arxiv.hep-th/0604181,
title = {6J Symbols Duality Relations},
author = {L. Freidel and K. Noui and P. Roche},
journal= {arXiv preprint arXiv:hep-th/0604181},
year = {2008}
}
备注
28 pages, 2 figures