caa a22 4500 606244417 CHVBK 20210128101330.0 cr unu---uuuuu 210128e20150201xx s 000 0 eng 10.1007/s12044-015-0211-1 doi (NATIONALLICENCE)springer-10.1007/s12044-015-0211-1 GOSWAMI DEBASHISH Indian Statistical Institute, 203, B. T. Road, 700 108, Kolkata, India aut Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups [Elektronische Daten] [DEBASHISH GOSWAMI] Let G be one of the classical compact, simple, centre-less, connected Lie groups of rank n with a maximal torus T, the Lie algebra G $\mathcal {G}$ and let {E i ,F i ,H i ,i=1, ,n} be the standard set of generators corresponding to a basis of the root system. Consider the adjoint-orbit space M={Ad g (H 1), g∈G}, identified with the homogeneous space G/L where L={g∈G: Ad g (H 1)=H 1}. We prove that the coordinate functions f i (g):=λ i (Ad g (H 1)), i=1, ,n, where {λ 1, ,λ n } is basis of G ′ ${\mathcal G}^{\prime }$ are ‘quadratically independent' in the sense that they do not satisfy any nontrivial homogeneous quadratic relations among them. Using this, it is proved that there is no genuine compact quantum group which can act faithfully on C(M) such that the action leaves invariant the linear span of the above coordinate functions. As a corollary, it is also shown that any compact quantum group having a faithful action on the noncommutative manifold obtained by Rieffel deformation of M satisfying a similar ‘linearity' condition must be a Rieffel-Wang type deformation of some compact group. Indian Academy of Sciences, 2015 Quantum isometry nationallicence compact quantum group nationallicence homogeneous spaces nationallicence simple Lie groups nationallicence Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 127-138 0253-4142 125:1<127 2015 125 12044 https://doi.org/10.1007/s12044-015-0211-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s12044-015-0211-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- GOSWAMI DEBASHISH Indian Statistical Institute, 203, B. T. Road, 700 108, Kolkata, India aut NATIONALLICENCE 773 0- Proceedings - Mathematical Sciences Springer India 125/1(2015-02-01), 127-138 0253-4142 125:1<127 2015 125 12044