On the Dihedral Cohomology of Graded Banach Algebras

  • Yousif Abdullah Alrashidi The Higher Institute of Telecommunications and Navigation
Keywords: Graded Banach algebras - dihedral cohomology.


We are concerned with the dihedral cohomology of a unital -graded Banach algebra  over  with a graded involution and study some properties of it. It is considered the prototype example of graded algebras with topology.


Arveson, W., An invitation to C*-algebras, Springer-Verlag, New York-Heidelberg, 1976.

Christensen, E. and Sinciair, A.M,. On the vanishing of for certain algebra, Pacific J. Math., 137 (1989), 55-63.

Dales, H.G., Banach algebras and automatic continuity, Clarendon Press, Oxford, 2000.

Gouda, Y.Gh., On the cyclic and dihedral cohomology of Banach spaces, Publ. Math. Debrecen 51/ 1-2 (1997), 67-80.

Gouda, Y.Gh., The relative dihedral homology of involutive algebras, Internat. J. Math. & Math. Sci. Vol.2, N0.4(1999) 807-815.

Gouda, Y.Gh., On the dihedral cohomology of operator algebra, Int. J. of algebra. Vol.4, No. 23(2010),1134-1144.

Johnson, B., Introduction to cohomology in Banach algebras. In: Algebras in Analysis. London, New York: Academic Press 1975.

Kassel, C., A Künneth formula for the cyclic cohomology of -graded algebras, Math. Ann.,257 (1986), 683-699.

Kassel, C., Homology and cohomology of associative algebras, -A concise introduction to cyclic homology-Advanced School on Non-commutative Geometry ICTP, Trieste, August 2004.

Krasauskas, R.L., Lapin, S.V. and Solov’ev, Yu. P., Dihedral homology and cohomology. Basic concepts and constructions, Mat. Sb. (N.S.) 133 (175) (1987), no. 1, 25–48, (Russian).

Megginson, R., An introduction to Banach space theory, (Springer-Verlag, New York, 1998).

How to Cite
Alrashidi, Y. (2016). On the Dihedral Cohomology of Graded Banach Algebras. Journal of Progressive Research in Mathematics, 10(1), 1425-1433. Retrieved from http://scitecresearch.com/journals/index.php/jprm/article/view/941