References
- Alaa, H. N. (2012, December). On the homology theory of operator algebras. International Journal of Mathematics and Mathematical Sciences, 1–17. https://doi.org/10.1155/2012/368527
- Alaa, H. N. (2019). On the relative dihedral cohomology of Banach algebras. Modern Applied Science, 13(10), 1-10. https://doi.org/10.5539/mas.v13n10p1
- Alaa, H. N., & Gouda, Y. G. (2011). Dihedral homology of polynomial algebras. International Journal of Algebras, 5(12), 569–578.
- Buchholtz, U., & Rijke, E. (2019). The long exact sequence of homotopy n-groups. Cornell university. https://arxiv.org/abs/1912.08696
- Cartan, H., & Eilenberg, S. (1956). Homological algebra. Princeton Mathematical.
- Connes, A. (1985). Non-commutative differential geometry. Publications mathématiques de l’IHÉS, 62(1), 41–144. https://doi.org/10.1007/BF02698807
- Cortiñas, G., & Valqui, C. (2003). Excision in bivariant periodic cyclic cohomology: A categorical approach. JOUR, 30, 167-201. https://doi.org/10.1023/B:KTHE.0000018383.93721.dd
- Goodwillie, T. (1985). Cyclic homology, derivations, and the free loopspace. Topology, 24(2), 187–215. https://doi.org/10.1016/0040-9383(85)90055-2
- Gouda, Y. G. (1997). On the cyclic and dihedral cohomology of Banach spaces. Publicationes Mathematicae-Debrecen, 51(1–2), 67–80.
- Gouda, Y. G. (2011). On the (co)homology theory of index category. Journal of the Egyptian Mathematical Society, 19(3), 137–141. https://doi.org/10.1016/j.joems.2011.12.002
- Gouda, Y. G., & Alaa, H. N. (2009). On the trivial and nontrivial cohomology with inner symmetry groups of some classes of operator algebras. International Journal of Mathematical Analysis, 3(8), 377–384.
- Guram, D., & Manuel, L. (2014, April). The excision theorems in Hochschild and cyclic homologies. Proceedings. Section A, Mathematics-The Royal Society of Edinburgh, 144 (2): 305–317. https://doi.org/10.1017/S0308210512001874
- Helemskii, A. Y. (1991). Banach cyclic (co)homology as Banach derived functors. St. Petersburg Mathematical Journal, 3 (5), 1149–1164. Algebra i Analiz, Volume 3, Issue 5, Pages 213–228 (Mi aa286). http://mi.mathnet.ru/eng/aa286
- Helemskii, A. Y. (1992). Banach cyclic (co)homology and the Connes-Tzygan exact sequence. Journal of the London Mathematical Society, s2-46(3), 449–462. https://doi.org/10.1112/jlms/s2-46.3.449
- Hochschild, G. (1945). On the cohomology groups of an associative algebra. The Annals of Mathematics, 46(1), 58–67. https://doi.org/10.2307/1969145
- Intissar, A. (2020). A mathematical study of a generalized SEIR model of COVID-19. SciMedicine Journal, 2, 30–67. [Special Issue “COVID-19”]. https://doi.org/10.28991/SciMedJ-2020-02-SI-4
- Johnson, B. E. (1972). Cohomology in Banach algebras. Providence, American mathematical Society, 1972 (Memoirs Amer. Math. Soc., 127). | MR 51 #11130 | Zbl 0256.18014
- Kostikov, Y., & Romanenkov, A. (2020, April). Approximation of the multidimensional optimal control problem for the heat equation (applicable to computational fluid dynamics (CFD)). Civil Engineering Journal, 6(4), 743–768. https://doi.org/10.28991/cej-2020-03091506
- Krasauskas, R. L., Lapin, S. V., & Solov’ev, Y. P. (1988). Dihedral homology and cohomology basic notions and constructions. Mathematics of the USSR-Sbornik, 61(1), P23–47. https://doi.org/10.1070/sm1988v061n01abeh003190
- Loday, J. (2013). Algebraic K-theory and cyclic homology. Journal of K-Theory, 11(3), 553–557. https://doi.org/10.1017/is012011006jkt200
- Loday, J.-L. (1998). Cyclic homology of algebras (Vol. 301). Springer. https://doi.org/10.1007/978-3-662-11389-9_2
- Lykova, Z. A., & Michael, C. W. (1998). Excision in the cohomology of Banach algebras with coefficients in dual bimodules. Banach Algebras, 97, 341–361. https://doi.org/10.1515/9783110802009.341
- Noreldeen, A. H. (2019). On the Hochschild cohomology theory of A∞-algebra. Scientific African, 5, e00115. https://doi.org/10.1016/j.sciaf.2019.e00115
- Penner, R. (2020). Long exact sequences of k-groups. Lecture Notes in Mathematics, 2262, 189-193. Springer. https://doi.org/10.1007/978-3-030-43996-5_36
- Quillen, D. (1972). On the cohomology and k-theory of the general linear groups over a finite field. The Annals of Mathematics, 96(3), 552–586. https://doi.org/10.2307/1970825
- Ralf, M. (2010). Excision in Hochschild and cyclic homology without continuous linear sections. Journal of Homotopy and Related Structures, 5(1), 269–303.
- Thiel, H. (2006). An introduction to Hochschild and cyclic homology. Term paper for Math 215B Algebraic Topology, Spring, UC Berkeley.
- Tsygan, B. L. (1983). The homology of matrix Lie algebras over rings and the Hochschild homology. Russian Mathematical Surveys, 38(2), 198–199. https://doi.org/10.1070/RM1983v038n02ABEH003481
- Tsygan, B. L. (1986). Homologies of some matrix Lie superalgebras. Functional Analysis and Its Applications, 20(2), 164–165. https://doi.org/10.1007/BF01077286
- Wodzicki, M. (1989). Excision in cyclic homology and in rational algebraic K-theory. The Annals of Mathematics, 129(3), 591–639. https://doi.org/10.2307/1971518