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

SIGMA 15 (2019), 082, 16 pages      arXiv:1904.03993      https://doi.org/10.3842/SIGMA.2019.082

One Parameter Family of Jordanian Twists

Daniel Meljanac a, Stjepan Meljanac b, Zoran Škoda c and Rina Štrajn d
a) Division of Materials Physics, Institute Rudjer Bošković, Bijenička cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia
b) Theoretical Physics Division, Institute Rudjer Bošković, Bijenička cesta 54, P.O. Box 180, HR-10002 Zagreb, Croatia
c) Department of Teachers' Education, University of Zadar, Franje Tudjmana 24, 23000 Zadar, Croatia
d) Department of Electrical Engineering and Computing, University of Dubrovnik, Ćira Carića 4, 20000 Dubrovnik, Croatia

Received April 16, 2019, in final form October 19, 2019; Published online October 25, 2019

Abstract
We propose an explicit generalization of the Jordanian twist proposed in $r$-symmetrized form by Giaquinto and Zhang. It is proved that this generalization satisfies the 2-cocycle condition. We present explicit formulas for the corresponding star product and twisted coproduct. Finally, we show that our generalization coincides with the twist obtained from the simple Jordanian twist by twisting by a 1-cochain.

Key words: noncommutative geometry; Jordanian twist.

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