Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 15 (2019), 054, 22 pages      arXiv:1812.05535      https://doi.org/10.3842/SIGMA.2019.054

Interpolations between Jordanian Twists Induced by Coboundary Twists

Andrzej Borowiec a, Daniel Meljanac b, Stjepan Meljanac c and Anna Pachoł d
a) Institute of Theoretical Physics, University of Wroclaw, pl. M. Borna 9, 50-204 Wroclaw, Poland
b) Division of Materials Physics, Ruder Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia
c) Division of Theoretical Physic, Ruder Bošković Institute, Bijenička c.54, HR-10002 Zagreb, Croatia
d) Queen Mary, University of London, Mile End Rd., London E1 4NS, UK

Received February 15, 2019, in final form July 11, 2019; Published online July 21, 2019

Abstract
We propose a new generalisation of the Jordanian twist (building on the previous idea from [Meljanac S., Meljanac D., Pachoł A., Pikutić D., J. Phys. A: Math. Theor. 50 (2017), 265201, 11 pages]). Obtained this way, the family of the Jordanian twists allows for interpolation between two simple Jordanian twists. This new version of the twist provides an example of a new type of star product and the realization for noncommutative coordinates. Real forms of new Jordanian deformations are also discussed. Exponential formulae, used to obtain coproducts and star products, are presented with details.

Key words: twist deformation; Hopf algebras; coboundary twists; star-products; real forms.

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