Amenable quase-lattice ordered groups and true representations
Abstract
Let (G, P) be a quasi-lattice ordered group. In [2] we constructed a universal covariant representation (A,U) for (G, P) in a way that avoids some of the intricacies of the other approaches in [11] and [8]. Then we showed if (G, P) is amenable, true representations of (G, P) generate C∗-algebras which are canonically isomorphic to the C∗-algebra generated by the universal covariant representation. In this paper, we discuss characterizations of amenability in a comparatively simple and natural way to introduce this formidable property. Amenability of (G, P) can be established by investigating the behavior of ΦU on the range of a positive, faithful, linear map rather than the whole algebra.
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References
R. Abu-Dawwas, More on crossed product over the support of graded rings, International Mathematical Forum, Vol. 5, No. 63 (2010), 3121-3126.
S. E. Atani and R. E. Atani, Graded multiplication modules and the graded ideal θg(M), Turk. J. Math, Vol. 35 (2011), 1-9. https://doi.org/10.3906/mat-0901-22
S. E. Atani and F. Farzalipour, Notes on the Graded Prime Submodules, International Mathematical Forum, 1 (2006), no. 38, 1871-1880. https://doi.org/10.12988/imf.2006.06162
R. Hazrat, Graded Rings and Graded Grothendieck Groups, Cambridge University Press, UK (2016). https://doi.org/10.1017/CBO9781316717134
F. Moh'D and M. Refai, More properties on flexible graded modules, Italian Journal of Pure and Applied Mathematics, 32(2014), 103-114.
C. Nastasescu, Group rings of graded rings. Applications , Journal of Pure and Applied Algebra , 33 (1984) 3 13-335. https://doi.org/10.1016/0022-4049(84)90065-3
C. Nastasescu and Van Oystaeyen, Graded Ring Theory, Mathematical library 28, North Holand, Amsterdam , (1982).
M. Refai, Augmented graded modules, Tishreen Univesity Journal for Studies and Scientific Research, 23(10)(2001), 231-245.
M. Refai, Augmented graded rings, Turkish Journal of Mathematics, 21(3)(1997), 333-341.
M. Refai and F. Moh'D, First strongly graded modules, Int. J. Math.: Game Theory and Algebra, 15(4)(2006), 451-457.
M. Refai and F. Moh'D, On flexible graded modules, Italian Journal of Pure and Applied Mathematics, 22(2007), 125-132.
M. Refai and M. Obeidat, On a strongly-supported graded rings, Mathematica Japonica Journal, 39(3) (1994), 519-522.
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