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Subgroups and subalgebras
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Related lectures (32)
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Lie Algebra: Vector Space and Multiplication Law
Covers Lie Algebra, focusing on vector space and multiplication law.
Universal Property of Groups
Explores the universal property of groups, defining homomorphisms and exploring subgroup properties.
Properties of the Exponential Map
Explores the properties of the exponential map in Lie groups and algebras.
Lie Algebra: Group Theory
Explores Lie Algebra's connection to Group Theory through associative operations and Jacobi identities.
Group Theory Basics
Introduces the basics of group theory, covering definitions, examples, subgroups, and homomorphisms.
Quotients of Linear Groups by Linearly Reductive Groups
Explores constructing quotients of linear algebraic groups by linearly reductive sub-groups.
Group Algebra: Maschke's Theorem
Explores Wedderburn's theorem, group algebras, and Maschke's theorem in the context of finite dimensional simple algebras and their endomorphisms.
Groups: Definitions, Properties, and Homomorphisms
Introduces the basic concepts of groups, including definitions, properties, and homomorphisms, with a focus on subgroup properties and normal subgroups.
Symmetry in Quantum Field Theory
Explores associativity, Lie algebra, Lie groups, relativity, and symmetry preservation in quantum field theory.
Lagrange's Theorem: Applications and Homomorphisms
Covers Lagrange's theorem, group homomorphisms, congruence classes, and normal subgroups.
