R matrix and bicovariant calculus for the inhomogeneous quantum groups IGLq(n)

Leonardo Castellani

doi:10.1016/0370-2693(93)91829-C

R matrix and bicovariant calculus for the inhomogeneous quantum groups IGL_q(n)

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Abstract

We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is GL_q(n), or its restrictions to SL_q(n), U_q(n) and SU_q(n). The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of homogeneous subgroup. A bicovariant differential calculus on IGL_q(n) is constructed, and its application to the D = 4 Poincaré group ISL_q(2, C) is discussed.

Original language	English
Pages (from-to)	335-338
Number of pages	4
Journal	Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics
Volume	298
Issue number	3-4
DOIs	https://doi.org/10.1016/0370-2693(93)91829-C
Publication status	Published - 14 Jan 1993
Externally published	Yes

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abstract = "We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is GLq(n), or its restrictions to SLq(n), Uq(n) and SUq(n). The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of homogeneous subgroup. A bicovariant differential calculus on IGLq(n) is constructed, and its application to the D = 4 Poincar{\'e} group ISLq(2, C) is discussed.",

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AB - We find the R matrix for the inhomogeneous quantum groups whose homogeneous part is GLq(n), or its restrictions to SLq(n), Uq(n) and SUq(n). The quantum Yang-Baxter equation for R holds because of the Hecke relation for the braiding matrix of homogeneous subgroup. A bicovariant differential calculus on IGLq(n) is constructed, and its application to the D = 4 Poincaré group ISLq(2, C) is discussed.

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ER -

R matrix and bicovariant calculus for the inhomogeneous quantum groups IGL_q(n)

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