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arXiv · hep-th/9210157

q-deformed conformal and Poincar{é} algebras on quantum 4-spinors

Tatsuo Kobayashi·Tsuneo Uematsu
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Abstract

We investigate quantum deformation of conformal algebras by constructing the quantum space for $sl_q(4,C)$. The differential calculus on the quantum space and the action of the quantum generators are studied. We derive deformed $su(4)$ and $su(2,2)$ algebras from the deformed $sl(4)$ algebra using the quantum 4-spinor and its conjugate spinor. The 6-vector in $so_q(4,2)$ is constructed as a tensor product of two sets of 4-spinors. The reality condition for the 6-vector and that for the generators are found. The q-deformed Poincar{é} algebra is extracted as a closed subalgebra.

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Tatsuo Kobayashi, Tsuneo Uematsu. 1992-10-30. q-deformed conformal and Poincar{é} algebras on quantum 4-spinors. https://doi.org/10.1007/bf01553014

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