Cohomology: Cross Product

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Related lectures (30)

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Decomposition of Group Algebras

Covers examples of group algebra decomposition and simple infinite-dimensional algebras.

Cohomology: Recollection and Foliations

Covers cohomology, injective resolutions, and acyclic objects in an abelian category.

Algebra: Chain Complexes

Explores chain complexes, abelian groups, homomorphisms, homology groups, and free abelian groups.

Chain Maps: Homotopy Invariance

Covers chain maps, homotopy invariance, homology groups, and induced homomorphisms between cycles and boundaries.

Zig Zag Lemma

Covers the Zig Zag Lemma and the long exact sequence of relative homology.

Homological Algebra: Basics and Applications

Covers the basics of Homological algebra, focusing on Ext modules and their significance in modern mathematics.

Ideals and Representations

Covers ideals, representations, modules, and maximal ideals in associative algebras.

Classification of Extensions

Explores the classification of extensions in group theory, emphasizing split extensions and semi-direct products.

Universal Coefficient Theorems

Delves into the universal coefficient theorems in homological algebra, showcasing their practical application in computing homology and cohomology groups.

Homotopy Theory in Chain Complexes

Explores acyclic fibrations and cylinder objects in chain complexes.