A note on Clifford-Klein forms

3Quantum: Algebra Geometry Information

物理学;数学

Jastrzbski, P.^1 ; Tralle, A.^1

Department of Mathematics and Information Technology, University of Warmia and Mazury, Sloneczna str. 54, Olsztyn

10-710, Poland^1

关键词: Automorphisms;    ClIFFORD;    Finite order;    Lie Algebra;    Strong regularities;    Subalgebras;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/532/1/012010/pdf
DOI  :  10.1088/1742-6596/532/1/012010

来源: IOP

【 摘 要 】

We consider the problem of finding Clifford-Klein forms in a class of homogeneous spaces determined by inclusions of real Lie algebras of a special type which we call strongly regular. This class of inclusions is described in terms of their Satake diagrams. For example, the complexifications of such inclusions contain the class of subalgebras generated by automorphisms of finite order. We show that the condition of strong regularity implies the restriction on the real rank of subalgebras. This in part explains why the known examples of Clifford-Klein forms are rare. We make detailed calculations of some known examples from the point of view of the Satake diagrams.