Embeddable quantum homogeneous spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:411

Article

Kasprzak, Pawel^1,2  Soltan, Piotr M.¹ 

[1] Univ Warsaw, Dept Math Methods Phys, Fac Phys, PL-00325 Warsaw, Poland

[2] Polish Acad Sci, Inst Math, PL-00956 Warsaw, Poland

关键词: Locally compact quantum group;    Quantum homogeneous space;    Closed quantum subgroup;   

DOI  :  10.1016/j.jmaa.2013.07.084

来源: Elsevier

【 摘 要 】

We discuss various notions generalizing the concept of a homogeneous space to the setting of locally compact quantum groups. On the von Neumann algebra level we recall an interesting duality for such objects studied earlier by M. lzumi, R. Longo, S. Popa for compact Kac algebras and by M. Enock in the general case of locally compact quantum groups. A definition of a quantum homogeneous space is proposed along the lines of the pioneering work of Vaes on induction and imprimitivity for locally compact quantum groups. The concept of an embeddable quantum homogeneous space is selected and discussed in detail as it seems to be the natural candidate for the quantum analog of classical homogeneous spaces. Among various examples we single out the quantum analog of the quotient of the Cartesian product of a quantum group with itself by the diagonal subgroup, analogs of quotients by compact subgroups as well as quantum analogs of trivial principal bundles. The former turns out to be an interesting application of the duality mentioned above. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free