Lectures related to G-modules and G-varieties

Introduces Lie algebras, vector spaces with a special bracket operation.

Explores Schur's lemma and its applications in representations of an associative algebra over an algebraically closed field.

Covers modern algebraic geometry, including algebraic sets, morphisms, and projective algebraic sets.

Covers the concept of group cohomology, focusing on chain complexes, cochain complexes, cup products, and group rings.

Explores various directions for studying algebraic groups and offers references for further exploration.

Covers simple modules, endomorphisms, and Schur's lemma in module theory.

Covers the properties of finite dimensional algebras and non-semisimple representations.

Introduces affine varieties and covers morphisms between them and their coordinate rings.

Covers linear algebraic groups, including special sets and matrix examples.

Covers affine algebraic sets, hypersurfaces, elliptic curves, ideals, and Noetherian rings in algebraic geometry.