全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

Monotileable Amenable Groups: An Application

DOI: 10.4236/oalib.1107012, PP. 1-15

Subject Areas: Mathematical Analysis

Keywords: Varieties of Groups, Abelian Groups, Multiplication, Amenable Groups, Lie Group, Folner Sequence

Full-Text   Cite this paper   Add to My Lib

Abstract

We study actions of countable discrete groups which are Monotileable amenable groups in the sense that there exists a mean on X which is invariant under the action of G. Assuming that G is nonamenable, we obtain structural results for the stabilizer subgroups of amenable actions which allow us to relate the first l2-Betti number of G with that of the stabilizer subgroups.

Cite this paper

Gaweash, A. M. A. , Bakur, H. Y. I. and Mulla, M. A. M. (2021). Monotileable Amenable Groups: An Application. Open Access Library Journal, 8, e7012. doi: http://dx.doi.org/10.4236/oalib.1107012.

References

[1]  Wehrfritz, B.A.F. (1969) In_nite Linear Groups. Springer, Berlin.
[2]  Luxemburg, W.A.J. (1969) Applications of Model Theory to Algebra, Analysis, and Probability. Holt, Rinehart and Winston, New York.
[3]  Neumnn, H. (1967) Varieties of Groups, Springer-Verlag, New York. https://doi.org/10.1007/978-3-642-88599-0
[4]  Arveson, W. (1976) An Invitation to C*-Algebras. Springer, New York.
[5]  Bekka, B., de la Harpe, P. and Valette, A. (2008) Kazhdan’s Property (T). Cambridge U. Press, Cambridge.
[6]  Dy, M.M. (1957) Amenable Semigroups. Illinois Journal of Mathematics, 1, 509-544. https://doi.org/10.1215/ijm/1255380675
[7]  Jean-Marie Normand Service de Physique Theorique, CEA/DSM/SPhT CNRS/ SPM/URA 2306 CEA/Saclay, F-91191 Gif-sur-Yvette Cedex, France.
[8]  Greenleaf, F.P. (1969) Invariant Means on Topological Groups. Van Nostrand, New York.
[9]  Fclnr, E. (1955) On Groups with Full Banach Mean Values. Mathematica Scandinavica, 3, 243-254. https://doi.org/10.7146/math.scand.a-10442
[10]  Brown, N.P. and Ozawa, N. (2008) C*-Algebras and Finite-Dimensional Approximations. Graduate Studies in Mathematics, 88. https://doi.org/10.1090/gsm/088

Full-Text


comments powered by Disqus

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133

WeChat 1538708413