Affine Lie Algebras and Loop Algebras
A detailed guide to affine lie algebras and loop algebras. Covers key methods, mathematical significance, and real-world applications.
Mathematics Category
Lie Algebras
51 articles
≈ 510 min total reading
Cartan Subalgebras and Root Systems
A detailed guide to cartan subalgebras and root systems. Covers key methods, mathematical significance, and real-world applications.
Casimir Element and Quadratic Casimir
A detailed guide to casimir element and quadratic casimir. Covers key methods, mathematical significance, and real-world applications.
Central Series and Nilpotent Lie Algebras
A detailed guide to central series and nilpotent lie algebras. Covers key methods, mathematical significance, and real-world applications.
Classification of Simple Lie Algebras
A detailed guide to classification of simple lie algebras. Covers key methods, mathematical significance, and real-world applications.
Definition of Lie Algebras and Bracket
A detailed guide to definition of lie algebras and bracket. Covers key methods, mathematical significance, and real-world applications.
Derivations and Outer Derivations
A detailed guide to derivations and outer derivations. Covers key methods, mathematical significance, and real-world applications.
Derived Series and Solvable Lie Algebras
A detailed guide to derived series and solvable lie algebras. Covers key methods, mathematical significance, and real-world applications.
Engel Theorem and Nilpotent Criteria
A detailed guide to engel theorem and nilpotent criteria. Covers key methods, mathematical significance, and real-world applications.
Enveloping Algebra and PBW Theorem
A detailed guide to enveloping algebra and pbw theorem. Covers key methods, mathematical significance, and real-world applications.
Examples of Lie Algebras in Mathematics
A detailed guide to examples of lie algebras in mathematics. Covers key methods, mathematical significance, and real-world applications.
Highest Weight Theory and Verma Modules
A detailed guide to highest weight theory and verma modules. Covers key methods, mathematical significance, and real-world applications.
Jacobson Radical and Structure Theory
A detailed guide to jacobson radical and structure theory. Covers key methods, mathematical significance, and real-world applications.
Jordan Decomposition in Lie Algebras
A detailed guide to jordan decomposition in lie algebras. Covers key methods, mathematical significance, and real-world applications.
Kac-Moody Algebras and Generalization
A detailed guide to kac-moody algebras and generalization. Covers key methods, mathematical significance, and real-world applications.
Killing Form and Invariant Bilinear Forms
A detailed guide to killing form and invariant bilinear forms. Covers key methods, mathematical significance, and real-world applications.
Lie Algebra Cohomology and Extensions
A detailed guide to lie algebra cohomology and extensions. Covers key methods, mathematical significance, and real-world applications.
Lie Algebra Cohomology with Coefficients
A detailed guide to lie algebra cohomology with coefficients. Covers key methods, mathematical significance, and real-world applications.
Lie Algebra Homomorphisms and Isomorphisms
A detailed guide to lie algebra homomorphisms and isomorphisms. Covers key methods, mathematical significance, and real-world applications.
Lie Algebra of a Lie Group Construction
A detailed guide to lie algebra of a lie group construction. Covers key methods, mathematical significance, and real-world applications.
Lie Algebra of Algebraic Groups
A detailed guide to lie algebra of algebraic groups. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Algebraic Geometry
A detailed guide to lie algebras in algebraic geometry. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Algebraic Number Theory
A detailed guide to lie algebras in algebraic number theory. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Algebraic Topology
A detailed guide to lie algebras in algebraic topology. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Classical Mechanics
A detailed guide to lie algebras in classical mechanics. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Coding Theory
A detailed guide to lie algebras in coding theory. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Control Theory
A detailed guide to lie algebras in control theory. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Differential Geometry
A detailed guide to lie algebras in differential geometry. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Machine Learning
A detailed guide to lie algebras in machine learning. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Number Theory
A detailed guide to lie algebras in number theory. Covers key methods, mathematical significance, and real-world applications.
Lie Algebras in Quantum Mechanics
A detailed guide to lie algebras in quantum mechanics. Covers key methods, mathematical significance, and real-world applications.
Quantum Groups as Deformed Lie Algebras
A detailed guide to quantum groups as deformed lie algebras. Covers key methods, mathematical significance, and real-world applications.
Representation Categories of Lie Algebras
A detailed guide to representation categories of lie algebras. Covers key methods, mathematical significance, and real-world applications.
Representation Ring of a Lie Algebra
A detailed guide to representation ring of a lie algebra. Covers key methods, mathematical significance, and real-world applications.
Representations of Lie Algebras
A detailed guide to representations of lie algebras. Covers key methods, mathematical significance, and real-world applications.
Restricted Lie Algebras in Characteristic P
A detailed guide to restricted lie algebras in characteristic p. Covers key methods, mathematical significance, and real-world applications.
Root Systems and Weyl Groups
A detailed guide to root systems and weyl groups. Covers key methods, mathematical significance, and real-world applications.
Root Systems and Weyl Groups (Lie Algebras)
A detailed guide to root systems and weyl groups (lie algebras). Covers key methods, mathematical significance, and real-world applications.
Root Vectors and Chevalley Basis
Learn about root vectors and chevalley basis — covering Root Vectors, Chevalley Basis, and the role of root vector in this fundamental mathematical topic.
Semidirect Products of Lie Algebras
A detailed guide to semidirect products of lie algebras. Covers key methods, mathematical significance, and real-world applications.
Semisimple Decompositions and Direct Sums
A detailed guide to semisimple decompositions and direct sums. Covers key methods, mathematical significance, and real-world applications.
Semisimple Lie Algebras and the Killing Form
A detailed guide to semisimple lie algebras and the killing form. Covers key methods, mathematical significance, and real-world applications.
Simple Lie Algebras over Fields of Characteristic
A detailed guide to simple lie algebras over fields of characteristic. Covers key methods, mathematical significance, and real-world applications.
Statement and Proof of Levi Decomposition
A detailed guide to statement and proof of levi decomposition. Covers key methods, mathematical significance, and real-world applications.
Subalgebras Ideals and Quotient Lie Algebras
A detailed guide to subalgebras ideals and quotient lie algebras. Covers key methods, mathematical significance, and real-world applications.
Tensor Products of Lie Algebra Modules
A detailed guide to tensor products of lie algebra modules. Covers key methods, mathematical significance, and real-world applications.
Toral Subalgebras and Maximal Toral
A detailed guide to toral subalgebras and maximal toral. Covers key methods, mathematical significance, and real-world applications.
Verma Modules and Category O
A detailed guide to verma modules and category o. Covers key methods, mathematical significance, and real-world applications.
Weights and Weight Spaces of Modules
A detailed guide to weights and weight spaces of modules. Covers key methods, mathematical significance, and real-world applications.
Weyl Character Formula for Representations
A detailed guide to weyl character formula for representations. Covers key methods, mathematical significance, and real-world applications.
Whitehead Lemma and Homological Algebra
A detailed guide to whitehead lemma and homological algebra. Covers key methods, mathematical significance, and real-world applications.