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Quantum deformation of relativistic supersymmetry. (English) Zbl 0908.17011
Slovák, Jan (ed.), Proceedings of the 15th Winter School on geometry and physics, Srní, Czech Republic, January 14–21, 1995. Palermo: Circolo Matemàtico di Palermo, Suppl. Rend. Circ. Mat. Palermo, II. Ser. 43, 207-216 (1996).
From the text: The author reviews recent research on quantum deformations of the Poincaré supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosiński, J. Lukierski, P. Maślanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct. As far as physics is concerned, the discussed deformations are closely related to quantum deformations of the (not super!) Poincaré group and algebra, which has become a subject of considerable interest in recent years. These deformations involve dimensional parameter \(\kappa\) (the classical case corresponds to the limit \(\kappa \to \infty)\) and some authors tried to impose limits on possible numerical values of \(\kappa\) coming from physical arguments.
For the entire collection see [Zbl 0884.00042].
17B37 Quantum groups (quantized enveloping algebras) and related deformations
16W30 Hopf algebras (associative rings and algebras) (MSC2000)
81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
81T60 Supersymmetric field theories in quantum mechanics