Liealgebrasstruktur
Liealgebrasstruktur refers to the structural aspects of Lie algebras, the algebraic objects that capture the symmetry of continuous groups. A Lie algebra over a field is a vector space equipped with a bilinear operation called the Lie bracket, denoted [·,·], that is alternating and satisfies the Jacobi identity. These properties make Lie algebras the linearized version of Lie groups, appearing in differential geometry, theoretical physics, and representation theory.
Basic structure theory classifies finite-dimensional Lie algebras into solvable, nilpotent, and semisimple types. The Levi decomposition
Representation theory studies linear actions of Lie algebras on vector spaces. The highest weight theory classifies
In physics, Lie algebras encode gauge symmetries and conserved quantities; for example, su(2) describes spin and
Key references include Humphreys, "Introduction to Lie Algebras and Representation Theory" and Serre, "Complex Semisimple Lie