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Lecture
The classical Lie algebras
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Related lectures (32)
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Lie Theorems and Group Algebra
Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.
Decomposition of Group Algebras
Covers examples of group algebra decomposition and simple infinite-dimensional algebras.
Lie Algebra: Vector Space and Multiplication Law
Covers Lie Algebra, focusing on vector space and multiplication law.
Nilpotent Lie Groups
Covers the properties of nilpotent Lie groups and the construction of non-degenerate alternating 2-forms.
Commutative Algebra: Recollections
Covers fundamental concepts in commutative algebra, including rings, units, zero divisors, and local rings.
Lie Algebras: Introduction and Structure
Introduces Lie algebras, vector spaces with a special bracket operation.
Ideals and Representations
Covers ideals, representations, modules, and maximal ideals in associative algebras.
Jacobi Identity in Lie Algebra
Explores the significance of the Jacobi identity in Lie algebra and its impact on linear vector spaces.
Simple Lie Algebras: Classification and Properties
Explores the classification and properties of simple complex Lie algebras, emphasizing their connection with Lie groups.
Integral Domains: Factorisation and Noetherian Rings
Explores factorisation in Principal Ideal Domains and Noetherian rings, emphasizing the integral closure concept and the factorisation of ideals in Dedekind rings.
