Construction of a compact quantum group for transposition-coloring function

• Autorzy: Kula A.
• Języki publikacji: EN

Abstrakty

EN

We apply the Woronowicz construction of compact quantum group to the function which associates different parameters (colors) with transpositions generating the set of four-element permutation.We show that in the case when one of the parameters equals one, we get a non-trivial (non-commutative) compact quantum group which is a twisted product of SU₋₁(2) and the two-dimensional torus.

Słowa kluczowe

EN

quantum groups; twisted determinant condition; twisted product

• Wydawca: Wrocław University of Science and Technology
• Czasopismo: Probability and Mathematical Statistics
• Rocznik: 2013
• Tom: Vol. 33, Fasc. 2
• Strony: 287--299
• Opis fizyczny: Bibliogr. 13 poz.

Twórcy

autor

Kula A.

• Institute of Mathematics, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław

Bibliografia

• [1] T. Banica and R. Speicher, Liberation of orthogonal Lie groups, Adv. Math. 222 (4) (2009), pp. 1461-1501.
• [2] S. Barlak, K-theory of SUq(2) for q = −1, available on arXiv:1302.0305v5 [math.OA].
• [3] A. Kula, Compact quantum group for transposition-coloring function II, in preparation.
• [4] P. Podleś and S. L. Woronowicz, Quantum deformation of Lorentz group, Comm. Math. Phys. 130 (1990), pp. 381-431.
• [5] M. Skeide, The Lévy-Khintchine formula for the quantum group SUq(2), PhD thesis, Heidelberg 1994.
• [6] P. M. Sołtan, Quantum Bohr compactification, Illinois J. Math. 49 (4) (2005), pp. 1245-1270.
• [7] Shuzhou Wang, Free products of compact quantum groups, Comm. Math. Phys. 167 (3) (1995), pp. 671-692.
• [8] S. L. Woronowicz, Compact matrix pseudogroups, Comm. Math. Phys. 111 (1987), pp. 613-665.
• [9] S. L. Woronowicz, Twisted SU(2) group. An example of a noncommutative differentia calculus, Publ. Res. Inst. Math. Sci. 23 (1) (1987), pp. 117-181.
• [10] S. L. Woronowicz, Tannaka-Kreĭn duality for compact matrix pseudogroups. Twisted SU(N) groups, Invent. Math. 93 (1) (1988), pp. 35-76.
• [11] J. Wysoczański, Twisted product structure and representation theory of the quantum group Uq(2), Rep. Math. Phys. 54 (3) (2004), pp. 327-347.
• [12] J. Wysoczański, On the Woronowicz’s twisted product construction of quantum groups, with comments on related cubic Hecke algebra, RIMS Kôkyûroku 1658 (2009), pp. 124-135.
• [13] S. Zakrzewski, Matrix pseudogroups associated with anti-commutative plane, Lett. Math. Phys. 21 (1991), pp. 309-321.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).