Lie Algebras

Some articles on lie, lie algebras, lie algebra, algebra:

Lorentz Invariance In Loop Quantum Gravity
... The compactness of the Lie group avoids some thus-far unsolved difficulties in the quantization of gauge theories of noncompact lie groups, and is responsible for the discreteness of the area and volume ... between SO(3) and SU(2) or between SO(3,1) and SL(2,C) at this level the respective Lie algebras are the same ... In fact, all four groups have the same complexified Lie algebra, which makes matters even more confusing (these subtleties are usually ignored in elementary ...
Lie Group Homomorphism
... In mathematics, a Lie group homomorphism is a map between Lie groups which is both a group homomorphism and a smooth map ... Lie group homomorphisms are the morphisms in the category of Lie groups ... In the case of complex Lie groups, one naturally requires homomorphisms to be holomorphic functions ...
Why Beauty Is Truth: A History Of Symmetry - Contents
... Gerolamo Cardano used algebra to solve the cubic and quartic equation ... Soldier and the Weakly Bookworm Marius Sophus Lie formalized Lie groups and Lie algebras ... Wilhelm Killing classified all simple Lie algebras (in what Ian Stewart calls the "greatest mathematical paper of all time") Chapter 11 The Clerk from the Patent Office Albert ...
Freudenthal Magic Square - Constructions - Triality
... Whereas Vinberg's construction is based on the automorphism groups of a division algebra A (or rather their Lie algebras of derivations), Barton and Sudbery use the group of automorphisms of ... by taking three copies of the division algebra A, and using the inner product on A to dualize the multiplication ... The following table compares its Lie algebra to the Lie algebra of derivations ...
Modular Lie Algebra
... In mathematics, a modular Lie algebra is a Lie algebra over a field of positive characteristic ... The theory of modular Lie algebras is significantly different from the theory of real and complex Lie algebras ... of the exponential map to establish a tight connection between properties of a modular Lie algebra and the corresponding algebraic group ...

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