Goswami, Debashish (2015) Quadratic independence of coordinate functions of certain homogeneous spaces and action of compact quantum groups Proceedings  Mathematical Sciences, 125 (1). pp. 127138. ISSN 02534142

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Official URL: http://www.ias.ac.in/describe/article/pmsc/125/01/...
Related URL: http://dx.doi.org/10.1007/s1204401502111
Abstract
Let G be one of the classical compact, simple, centreless, connected Lie groups of rank n with a maximal torus T, the Lie algebra 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 adjointorbit 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′ 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 RieffelWang type deformation of some compact group.
Item Type:  Article 

Source:  Copyright of this article belongs to Indian Academy of Sciences. 
Keywords:  Quantum Isometry; Compact Quantum Group; Homogeneous Spaces; Simple Lie Groups 
ID Code:  102139 
Deposited On:  01 Feb 2018 04:35 
Last Modified:  01 Feb 2018 04:35 
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