Spectral triples of weighted groups
الموضوعات :M. Amini 1 , Kh. Shamsolkotabi 2
1 - Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
2 - Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran 14115-134, Iran
الکلمات المفتاحية: Spectral triple, weighted group, functors,
ملخص المقالة :
We study spectral triples on (weighted) groups and consider functors between the categories of weighted groups and spectral triples. We study the properties of weights and the corresponding functor for spectral triples coming from discrete weighted groups.
[1] M. Amini, K. Shamsolkotabi, Spectral geometry of weighted groups, preprint.
[2] W. Arendt, R. Nittka, W. Peter, F. Steiner, Weyls law: Spectral properties of the Laplacian in Mathematics and Physics, in: Mathematical analysis of evolution, information, and complexity, W. Arendt and W.P. Schleich (Eds.), Wiley-VCH, Weinheim, (2009), 1-71.
[3] P. Bertozzini, R. Conti, W. Lewkeeratiyutkul, A category of spectral triples and discrete groups with length function, Osaka J. Math. 43 (2) (2006), 327-350.
[4] P. Bertozzini, R. Conti, W. Lewkeeratiyutkul, Categorical non-commutative geometry, Journal of Physics: Conference Series. 346 (2012), 1-9.
[5] A. Connes, Noncommutative geometry, Academic Press, New York, 1994.
[6] A. Connes, Noncommutative geometry and reality, J. Math. Phys. 36 (11) (1995), 6194-6231.
[7] A. Connes, Compact metric spaces, Fredholm modules and hyperfiniteness, Ergodic Theory Dynam. Systems. 9 (1989), 207-220.
[8] A. Connes, On the spectral characterization of manifolds, (2008), arXiv:0810.2088.
[9] A. Connes, H. Moscovici, The local index formula in noncommutative geometry, Geometry and Funct. Analysis. 5 (1995), 174-243.
[10] J. M. Gracia-Bondia, H. Figueroa, J.C. Varilly, Elements of noncommutative geometry, Birkhauser, Boston, 2000.
[11] V. Ivrii, 100 years of Weyl's law, Bulletin of Mathematical Sciences. 6 (2016), 379-452.
[12] M. Kac, Can one hear the shape of a drum?, Amer. Math. Monthly. 73 (1966), 1-23.
[13] H. A. Lorentz, Alte und neue fragen der Physik, Physikal. Zeitschr. 11 (1910), 1234-1257.
[14] A. Sommerfeld, Die Greensche funktion der schwingungsgleichung fur ein beliebiges gebiet, Physikal. Zeitschr. 11 (1910), 1057-1066.
[15] H. Weyl, Uber die asymptotische verteilung der eigenwerte, Nachr. Konigl. Ges. Wiss. Gottingen. (1911), 110-117.
[16] H. Weyl, Das asymptotische verteilungsgesetz linearen partiellen differentialgleichungen, Math. Ann. 71 (1912), 441-479.
[17] H. Weyl, Uber die abhangigkeit der eigenschwingungen einer membran von deren begrenzung, J. Reine Angew. Math. 141 (1912), 1-11.
[18] H. Weyl, Uber die randwertaufgabe der strahlungstheorie und asymptotische spektralgeometrie, J. Reine Angew. Math. 143 (1913), 177-202.
[19] H. Weyl, Das asymptotische verteilungsgesetz der eigenschwingungen eines beliebig gestalteten elastischen korpers, Rend. Circ. Mat. Palermo. 39 (1915), 1-49.
