On the vanishing cohomology theory of some operator algebras
Keywords:
Dihedral homology – Stable algebras - C^*-algebra -cohomology.
Abstract
We concerned with the vanishing of the dihedral and reflexive cohomology groups of stable -algebra. Wodzicki has proved that the cyclic cohomology of stable -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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[14] Alaa Hassan Noreldeen, Differential graded algebras and derived E∞-algebras, Appl. Math. Inf. Sci. 14, No. 4, 673-678 (2020)
[15] Alaa Hassan & Hegagi M. Ali and Samar Aboquota, (Some properties in the (co)homology theory of lie algebra), Aust. J. Math. Anal. Appl., Vol. 17 (2020), No. 2, Art. 9, 9 pp., ISSN: 1449-5910
[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] Alaa H. N. Mohamed & Mohsen A. H. Eid, "Study of the homology theory of fuzzy algebra", International J. of Research, Volume 06, Issue, 3March 2019.
[9] Alaa Hassan Noreldeen Mohamed, "On the cohomology of relative Banach algebras", Modern Applied Science; Vol. 13, No. 10; 2019. doi:10.5539/mas. v13n10p1.
[10] Alaa H. N. Mohamed, "Study of the d-infinity differential module" International Journal of Mathematical Analysis, Vol. 13, 2019, no. 10, 487 – 494, https://doi.org/10.12988/ijma.2019.9849.
[11] Alaa Hassan Noreldeen and S. A. Abo-Quota, "Operations on the dihedral homology theory", Applied Mathematical Sciences, Vol. 13, 2019, no. 20, 983 – 990. https://doi.org/10.12988/ams.2019.98122.
[12] Alaa Hassan Noreldeen, Treatment of operator algebras through cohomology theory, Inf. Sci. Lett. 9, No. 1, 1-5 (2020).
[13] Alaa Hassan Noreldeen Mohamed, Perturbation differential a-infinity algebra, Appl. Math. Inf. Sci. 14, No. 3, 1-5 (2020), http://dx.doi.org/10.18576/amis/Alaa
[14] Alaa Hassan Noreldeen, Differential graded algebras and derived E∞-algebras, Appl. Math. Inf. Sci. 14, No. 4, 673-678 (2020)
[15] Alaa Hassan & Hegagi M. Ali and Samar Aboquota, (Some properties in the (co)homology theory of lie algebra), Aust. J. Math. Anal. Appl., Vol. 17 (2020), No. 2, Art. 9, 9 pp., ISSN: 1449-5910
Published
2021-08-03
How to Cite
Alrashidi, Y. (2021). On the vanishing cohomology theory of some operator algebras. Journal of Progressive Research in Mathematics, 18(3), 24-30. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/2080
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