Concept

Lie algebra cohomology

Related lectures (29)

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Quantum Field Theory: BRST Symmetry

Covers the BRST symmetry in Quantum Field Theory, focusing on physical states and norm preservation.

Differential Forms Integration

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.

Group Cohomology

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

Cohomology Groups: Hopf Formula

Explores the Hopf formula in cohomology groups, emphasizing the 4-term exact sequence and its implications.

Cross Product in Cohomology

Explores the cross product in cohomology, covering its properties and applications in homotopy.

Cohomology Real Projective Space

Covers cohomology in real projective spaces, focusing on associative properties and algebraic structures.

Curl and Exact Sequences

Covers the concept of curl in vector calculus and De Rham cohomology.

Cohomology: Abelian Cochains

Introduces cohomology, focusing on abelian cochains and their correspondence with singular cochains.

Homology of Projective Space

Covers the homology of projective space, focusing on cohomology and exact sequences.

Topology Seminar: Tower Sequences and Homomorphisms

Explores tower sequences, homomorphisms, and their applications in topology, including the computation of homology and the construction of telescopes.

Cohomology of C2: Cup Product

Covers the cup product in the cohomology of C2, showing how non-trivial elements are represented by cocycles.

Acyclic Models: Cup Product and Cohomology

Covers the cup product on cohomology, acyclic models, and the universal coefficient theorem.

Algebraic Kunneth Theorem

Covers the Algebraic Kunneth Theorem, explaining chain complexes and cohomology computations.

Cohomology: Cup Product

Covers the cup product in cohomology, focusing on examples and computations.

Quantum Field Theory: Poincaré Group

Explores Einsteinian relativity, the Lorentz group, and Poincaré transformations, emphasizing proper and non-orthochronous components.

Graded Ring Structure on Cohomology

Explores the associative and commutative properties of the cup product in cohomology, with a focus on graded structures.

Homological Algebra: Basics and Applications

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

Cohomology: Recollection and Foliations

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

Vector Fields

Explains vector fields as derivations and their algebraic structure in Lie algebra.