Abstract
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.
Highlights
Algebraic topology is one of the main areas in mathematics
This study concentrates on cohomology groups for associative algebras
Main Results: This section is devoted to computing the zerocohomology groups H0(A, A) and firstcohomology groups H1(A, A) of fourdimensional nilpotent associative algebras
Summary
Algebraic topology is one of the main areas in mathematics This area uses fundamental ingredients from abstract algebra in the study of topological spaces. One of the essential techniques of algebraic topology is cohomology groups It is a general term of a sequence of groups associated with a topological space which is defined from a cochain. One of the ancient areas of the modern algebra is the theory of finite-dimensional associative algebras, and it has been studied by many investigators like Pierce 1, Mazzola 2 and Basri 3. In this regard, this study concentrates on cohomology groups for associative algebras
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