homological algebra


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homological algebra

[¦hä·mə¦läj·ə·kəl ′al·jə·brə]
(mathematics)
The study of the structure of modules, particularly by means of exact sequences; it has application to the study of a topological space via its homology groups.
References in periodicals archive ?
Sven, who joined Teesside University in 2018, will be focusing on the 'hearts of karoubian categories', a project covering the areas of homological algebra and functional analysis.
The lectures cover randomized numerical linear algebra, optimization algorithms for data analysis, introductory stochastic optimization, randomized methods for matrix computations, probabilistic methods for data science, and homological algebra and data.
The representation theory of Cherednik algebras has strong connections to algebraic geometry, combinatorics, finite dimensional algebra, homological algebra, integrable systems, Lie theory, noncommutative algebra and q calculus; they have been used to confirm conjectures and answer questions in all of these subjects.
Stammbach, A Course in Homological Algebra, Springer, Berlin, Germany, 1971.
Some notions of homological algebra should be recalled from [3, 13], in order to formulate the next result.
He assumes students are familiar with homological algebra, algebraic topology based on different forms, and de Rham cohomology.
We present here a synopsis of the results together with applications of this beautiful interplay between combinatorial topology and homological algebra.
This two-volume research monograph on the general Lagrangian Floer theory and the accompanying homological algebra of filtered $A_\infty$-algebras provides the most important step towards a rigorous foundation of the Fukaya category in general context.
Davis, A vanishing theorem in homological algebra, Comment.
For example, set theory was invented in order to help in analysing the convergence behaviour of Fourier series; homological algebra was invented in order to serve algebraic topology, and category theory was first developed with the view of applying it in homological algebra (as well as algebraic topology and algebraic geometry).