摘要We investigate the inhomogeneous invariance quantum group of the d−dimensional d−parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d−parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.
Abstract：We investigate the inhomogeneous invariance quantum group of the d−dimensional d−parameter deformed boson algebra. It is found that the homogeneous part of this quantum group is given by the d−parameter deformed general linear group. We construct the R-matrix which collects all information about the non-commuting structure of the quantum group for the two-dimensional case.
[1] Arik M, Coon D D and Lam Y M 1975 J. Math. Phys. 16 1776 [2] Arik M and Coon D D 1976 J. Math. Phys. 17 524 [3] Macfarlane A J 1989 J. Phys. A 22 4581 [4] Biedenharn L C 1989 J. Phys. A L873 [5] Sklyanin E, Takhtajan L and Faddeev L 1979 Theor. Math. Phys. 40 688 [6] Kulish P and Reshetikhin N Y 1983 J. Sov. Math. 23 2345 [7] Chacihian M and Demichev A P 1996 Introduction to Quantum Groups (River Edge, NJ: World Scientific) [8] Biedenharn L C and Lohe M A 1995 Quantum Group Symmetry and q Tensor Algebras (Singapore: World Scientific) [9] Faddeev L D, Reshetikhin N Y and Takhtajan L A 1990 Leningrad Math. J. 1 193 [10] Arik M and Arikan A S 2001 Eur. Phys. J. C 20 389 [11] Woronowicz S L 1987 Commun. Math. Phys. 111 613 [12] Manin Yu I 1988 Quantum Groups and Non Commutative Geometry (Montreal: Centre de Reserches Mathematiques) [13] Arik M and Kayserilioglu U 2005 Balkan Phys. Lett. 13 101 [14] Arik M, Gun S and Yildiz A 2003 Eur. Phys. J. C 27 453 [15] Arik M and Baykal A 2004 J. Math. Phys. 45 4207 [16] Altintas A A, Arik M and Arikan A S 2009 Mod. Phys. Lett. A 24 3137 [17] Schirmacher A 1991 Z. Phys. C 50 321 [18] Altintas A A, Arik M and Arikan A S 2010 Central Eur. J. Phys. 8 819
2012, Vol. 29 
