Cohomology of groups with normal Engel subgroups by Kissin, Edward, Shulman, Victor S.

“…The paper contains several results on the structure of 1-cocycles and the first cohomology group for a pair of representations of a connected group with a normal Engel subgroup.…”
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On cohomologies and representations of groups with normal Engel subgroups by Kissin, Edward, Shulman, Victor

“…The paper studies triviality conditions for the cohomology group H1(G; lambda;U) when lambda and U are sectionally spectrally disjoint and examines some decompositions of the extension e(lambda; U; ksi) of lambda by U associated with non-trivial (lambda; U)-cocycles ksi.…”
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Cohomological approach to classify nilpotent Leibniz algebras. by Rakhimov , I.S., Kamel , A.M. Atan, Sapar, Siti Hasana

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Cohomology and extensions of representations of groups with normal Engel subgroups by Kissin, Edward, Shulman, Victor

“…The paper studies the first cohomology group H1 (G, λ, U) under various spectral type conditions imposed on the restrictions of λ, U to N. …”
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A cohomological approach for classifying nilpotent Leibniz algebras by Rakhimov , Isamiddin Sattarovich, Langari, Seyed Jalal

“…In this paper a cohomological approach (the Skjelbred-Sund method)to classify nilpotent Leibniz algebras in low dimensional cases will be presented. …”
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Cohomology spaces of low dimensional complex associative algebras by Mohammed, Nadia F., Isamiddin, Rakhimov, Said Husain, Sharifah Kartini

“…In this paper, we calculate cohomology groups of low-dimensional complex associative algebras. …”
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Representations of nilpotent groups: extensions, neutral cohomology, and Pontryagin spaces by Kissin, Edward, Shulman, Victor S.

“…Spectral criteria for the cohomological triviality of extensions of representations of connected nilpotent groups are obtained. …”
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Non-unitary representations of nilpotent groups, I: Cohomologies, extensions and neutral cocycles by Kissin, Edward, Shulman, Victor S.

“…We investigate the structure of the extensions of λby Uand, correspondingly, the group H1(λ, U)of 1-cohomologies. A spectral criterion of triviality of H1(λ, U)is proved and systematically used in the study of various types of decomposition of the extensions. …”
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ALJABAR HOMOLOGIS ATAS MODUL: TOR DAN EXT by , RAMLI, S.Si., , Dr. Budi Surodjo, M.Si.

“…In this thesis we construct the homology and cohomology functors, also the long exact sequence of homology and cohomology modules. …”

Group actions and their applications in associative algebras and algebraic statistics by Mohammed, Nadia Faiq

“…In the first part, we consider an action of associative algebra A on a vector space to study low-dimensional cohomology groups of associative algebras. The origin of cohomology groups is found in algebraic topology. …”
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Classification Of Low Dimensional Nilpotent Leibniz Algebras Using Central Extensions by Langari, Seyed Jalal

“…Loday (1993) are non-antisymmetric generalizations of Lie algebras. There is a cohomology theory for these algebraic objects whose properties are similar to those of the classical Chevalley-Eilenberg cohomology theory for Lie algebras. …”
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Central extension of low dimensional associative and Leibniz algebras by Ab Rahman, Nurnazhifa

“…Leibniz algebras was introduced by Louis Loday due to several considerations in algebraic K-theory. The cyclic cohomology was somehow related to Lie algebra homology. …”
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Bornological structures on some algebraic systems by Imran, Anwar Nooraldeen

“…For this purpose, we construct chorology theory for bornological groups based on bounded cochains and study some of its basic properties. We show that the cohomology theory of bounded cochains and the cohomology theory of homogenous cochains are isomorphic. …”
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On central extensions of Nulfilioform Leibniz algebras. by Sattarovich, Rakhimov Isamiddin, Langari, Seyed Jalal, Langari, Mouna Bibi

“…We establish a bijective correspondence between all central extensions of fixed Leibniz algebra L by V (with k−dimensional centers), and certain orbits in the set of all k−dimensional subspaces in the second cohomology group H2(L, V ), under the canonical action of Aut(L). …”

On central extensions of associative dialgebras by Rakhimov, Isamiddin S.

“…In 1978 Skjelbred and Sund reduced the classification of nilpotent Lie algebras in a given dimension to the study of orbits under the action of automorphism group on the space of second degree cohomology of a smaller Lie algebra with coefficients in a trivial module. …”
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Central Extensions of Nilpotent Lie and Leibniz Algebras by Langari, Mouna Bibi

“…In order to locate a basis for second cohomology group of Lie algebras, the researcher must locate cocycles as well as coboundary. …”
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Representations of nilpotent groups on spaces with indefinite metric by Kissin, Edward, Shulman, Victor S.

“…So their study is based on some special cohomological technique. We concentrate mostly on the problems of the decomposition of these representations and the classification of “non-decomposable” ones.…”
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