On the vanishing of the cohomology of stable C*-algebras
Keywords:
Dihedral homology – Stable algebras - C^*-algebra -cohomology.
Abstract
We concerned with the vanishing of the dihedral and reflexive cohomology groups of stable C*-algebra. Wodzicki has proved that, the cyclic cohomology of stable C*-algebra is vanished. We extend this fact to prove that the reflexive and dihedral cohomology of this class are also vanish.
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References
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[12] A. Ya. Helemskii " the homology in Banach and topological algebras" Kluwer Acd. Press (1989).
[13] B. E. Johnson “Cohomology of operator algebras” Memoirs. Amer. Math. Soc. No. 127 (1972).
[14] J-L. Loday "cyclic homology" Second Springer-Verlag, New York (1998).
[15] M. Wodzicki “Vanishing of cyclic homology of stable C*-algebras” C. R. Acad. Sci. Paris, 307, Serie I, (1988),329-334.
[2] Alaa H. N., "On the relative dihedral cohomology of Banach algebras", Modern Applied Science; 2019, Vol. 13, No. 10; DOI: 10.5539/mas. v13n10p1.
[3] Loday J-L., "Cyclic Homology of Algebras", Springer Berlin Heidelberg, (1998), vol 301., https://doi.org/10.1007/978-3-662-11389-9_2.
[4] Thiel H., "An introduction to hochschild and cyclic homology", Term paper for Math 215B Algebraic Topology”, Spring 2006, UC Berkeley.
[5] Y. Gh. Gouda, The relative dihedral homology of involutive algebras, Internat. J. Math. & Math. Sci. Vol.2, N0.4(1999) 807-815.
[6] Krasauskas R L, & Lapin S V, & Solov'ev Yu P, "Dihedral homology and cohomology basic notions and constructions", Mathematics of the USSR-Sbornik , 1988, volume 61, issue 1, P23-47 . DOI: 10.1070/sm1988v061n01abeh003190.
[7] E. Christensen and A. M. Sinclair, “On the vanishing of Hn (A, A*) for certain c*-algebras”. Pacific J. of Math. 137, No. 1. (1989), 55-63.
[8] G. Frederic and White M.C “Vanishing of the third simplicial Cohomology group ” Trans. A.M.s., 353, No 5(2001),2003-2017.
[9] Y. Gh. Gouda "Reflexive and dihedral (co)homology of pre-additive category " Int. J. of Math, & Math. Sci 24:7 (2001), 429-438.
[10] Y. Gh. Gouda "On the cohomology wit inner symmetry of operator algebra" Differential homology and Dynamic System, 2008.
[11] Y. Gh. Gouda "On the cohomology of certain c*-algebra" ASW. Sc. Tec. Bull.,19 (1998), 26-30.
[12] A. Ya. Helemskii " the homology in Banach and topological algebras" Kluwer Acd. Press (1989).
[13] B. E. Johnson “Cohomology of operator algebras” Memoirs. Amer. Math. Soc. No. 127 (1972).
[14] J-L. Loday "cyclic homology" Second Springer-Verlag, New York (1998).
[15] M. Wodzicki “Vanishing of cyclic homology of stable C*-algebras” C. R. Acad. Sci. Paris, 307, Serie I, (1988),329-334.
Published
2021-06-03
How to Cite
Alrashidi, Y. (2021). On the vanishing of the cohomology of stable C*-algebras. Journal of Progressive Research in Mathematics, 18(2), 39-44. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2048
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