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arXiv · q-alg/9507005

Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters

Jerzy Lukierski·Pierre Minnaert·Marek Mozrzymas
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Abstract

We consider new class of classical r-matrices for D=3 and D=4 conformal Lie algebras. These r-matrices do satisfy the classical Yang-Baxter equation and as two-tensors belong to the tensor product of Borel subalgebra. In such a way we generalize the lowest order of known nonstandard quantum deformation of sl(2) to the Lie algebras sp(4) = so(5) and sl(4) = so(6). As an exercise we interpret nonstandard deformation of sl(2) as describing quantum D=1 conformal algebra with fundamental mass parameter. Further we describe the D=3 and D=4 conformal bialgebras with deformation parameters equal to the inverse of fundamental masses. It appears that for D=4 the deformation of the Poincare algebra sector coincides with "null plane" quantum Poincare algebra.

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Jerzy Lukierski, Pierre Minnaert, Marek Mozrzymas. 1995-07-10. Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters. https://doi.org/10.1016/0370-2693(96)01604-8

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