Abstract
We find an explicit formula for finding pairs of cocycles for the construction of examples of locally compact quantum groups by using the bicrossed product of Lie groups.
Similar content being viewed by others
References
G. I. Kac, “Extensions of groups that are ring groups,” Mat. Sb., 76, No. 3, 473–496 (1968).
S. Vaes and L. Vainerman, “Extensions of locally compact quantum groups and the bicrossed product construction,” Adv. Math., 175, No. 1, 1–101 (2003).
S. Majid, Foundations of Quantum Group Theory, Cambridge University Press, Cambridge (1995).
S. Baaj, G. Skandalis, and S. Vaes, Topological Kac Cohomology for Bicrossed Products, http://arxiv.org/math.QA/0307172.
Yu. A. Chapovsky, A. A. Kalyuzhnyi, and G. B. Podkolzin, “On the group of extensions for the bicrossed product construction for a locally compact group,” Algebra Discrete Math., 3, 12–19 (2004).
A. A. Kalyuzhnyi, G. B. Podkolzin, Yu. A. Chapovskii, “Construction of cocycles for a bicrossed product of Lie groups,” Funkts. Anal. Prilozhen., 40, No. 2, 70–73 (2006).
A. Guichardet, Cohomologie des Groupes Topologiques et des Algèbres de Lie, CEDIC, Paris (1984).
Yu. A. Chapovsky, A. A. Kalyuzhnyi, and G. B. Podkolzin, “On 2 + 2 locally compact quantum groups,” in: Proceedings of the Institute of Mathematics, Ukrainian National Academy of Sciences, Vol. 50, Part 3 (2004), pp. 1064–1070.
Author information
Authors and Affiliations
Additional information
__________
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 59, No. 11, pp. 1510–1522, November, 2007.
Rights and permissions
About this article
Cite this article
Kalyuzhnyi, A.A., Podkolzin, G.B. & Chapovskii, Y.A. Finding cocycles in the bicrossed product construction for Lie groups. Ukr Math J 59, 1693–1707 (2007). https://doi.org/10.1007/s11253-008-0019-6
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11253-008-0019-6