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The study of cohomology groups is one of the most intensive and exciting researches that arises from algebraic topology. Particularly, the dimension of cohomology groups is a highly useful invariant which plays a rigorous role in the geometric classification of associative algebras. This work focuses on the applications of low dimensional cohomology groups. In this regards, the cohomology groups of degree zero and degree one of nilpotent associative algebras in dimension four are described in matrix form.
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Peirce B. Linear associative algebra. Am J Math. 1881 Jan 1;4(1):97-229.
Mazzola G. The algebraic and geometric classification of associative algebras of dimension five Manuscr Math. 1979 Mar 1;27(1):81-101
Basri W. Classification and derivations of low- dimensional complex dialgebras. Serdang: Universiti Putra Malaysia; 2014.
Mohammed NF, Rakhimov IS, Hussain SK. Cohomology spaces of low dimensional complex associative algebras. In AIP Conference Proceedings. 2017 Apr 27; 1830(1): 070031. AIP Publishing LLC. Available from: https://aip.scitation.org DOI: abs/10.1063/1.4980980
Mohammed NF, Rakhimov IS, Husain SK. Contractions of low dimensional complex associative algebras. In AIP Conference Proceedings. 2017 Jan 10; 1795(1): 020022. AIP Publishing LLC. Available from: https://aip.scitation.org DOI: 10.1063/1.4972166
Mohammed NF, Rakhimov IS, Said Husain SK. On Contractions of Three-Dimensional Complex Associative Algebras. J Generalized Lie Theory Appl. 2017;11(282):2.
Hochschild G. On the cohomology groups of an associative algebra. Ann Math. 1945 Jan; 46(1):58-67. Available from: https://www.jstor.org/stable/i307222 DOI: 10.2307/1969145
Mohammed M A. H. Derivations and Centroids of Finite Dimensional Dialgebras. Serdang: Universiti Putra Malaysia; 2016.
Abdulkareem AO, Fiidow MA, Rakhimov IS. Derivations and Centroids of Four-dimensional Associative Algebras. Int J Pure Appl Math.2017; 112(4):655-671. Available from: https://ijpam.eu/contents/2017-112-4/1/index.html DOI: 10.12732/ijpam.v112i4.
Pierce RS. Associative Algebras, New York, Springer, 1982