In algebra, Weyl's theorem on complete reducibility is a fundamental result in the theory of Lie algebra representations (specifically in the representation...

theory, "semi-simplicity" is also called complete reducibility. For example, Weyl's theorem on complete reducibility says a finite-dimensional representation...

mathematics, Weyl's theorem or Weyl's lemma might refer to one of a number of results of Hermann Weyl. These include the Peter–Weyl theorem Weyl's theorem on complete...

complex-valued functions on G, and thus also in the space L2(G) of square-integrable functions. The second part asserts the complete reducibility of unitary representations...

infinite-dimensional; the group is not semisimple and it does not satisfy Weyl's theorem on complete reducibility.) It was introduced by Eugene Wigner, to classify particles...

MathWorld. Weisstein, Eric W. "Weyl's Criterion". MathWorld. Weyl's Criterion at PlanetMath. Lecture notes by Charles Walkden with proof of Weyl's Criterion...

of a Lie group Weight (representation theory) Weyl's theorem on complete reducibility Root system Weyl character formula Representation theory of a connected...

be applied to show complete reducibility of representations for such groups via the construction of an invariant inner product. Weyl extended Schur's method...

This observation plays an important role in the proof of Weyl's theorem on complete reducibility. It is also possible to prove the nonvanishing of the eigenvalue...

Whitehead lemma is an important step toward the proof of Weyl's theorem on complete reducibility. Without mentioning cohomology groups, one can state Whitehead's...

(This is proved as a consequence of Weyl's complete reducibility theorem; see Weyl's theorem on complete reducibility#Application: preservation of Jordan...

Lie algebras are distinguished from the tensor representations given by Weyl's construction by the weights. Whereas the weights of the tensor representations...

characteristic not dividing the order of G is semisimple. By Weyl's theorem on complete reducibility, every finite-dimensional representation of a semisimple...

classification of representations reduces to the classification of irreducible representations. See Weyl's theorem on complete reducibility. If we have two representations...

K has characteristic 0 this was well known; in fact Weyl's theorem on the complete reducibility of the representations of G implies that F can even be...

Weyl's lemma on hypoellipticity Weyl's paradox (properly the Grelling–Nelson paradox) Weyl's postulate Weyl's theorem on complete reducibility Weyl's...

and was Weyl's original argument for what is now called Weyl's theorem. There is also a purely algebraic argument for the complete reducibility of representations...

In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, is a theorem relating the flux of a vector field through...

In representation theory, the Peter–Weyl theorem guarantees that any unitary representation of a compact group on a Hilbert space splits as the direct...

in quantum mechanics since the 1920s, particularly influenced by Hermann Weyl's 1928 book Gruppentheorie und Quantenmechanik. One of the pioneers in constructing...

finally, as do Russell and Whitehead, axioms of infinity, reducibility, or completeness, which in fact are actual, contentual assumptions that cannot...

some theorems that cannot be proven in common axiom systems for set theory. Contemporary work in the foundations of mathematics often focuses on establishing...

second theorems, which are fundamental in mathematical physics. Noether was described by Pavel Alexandrov, Albert Einstein, Jean Dieudonné, Hermann Weyl and...

written his articles on operator theory, and the application of this work was instrumental in his mean ergodic theorem. The theorem is about arbitrary one-parameter...

Russell postulated his axiom of reducibility. But, Kleene wonders, "on what grounds should we believe in the axiom of reducibility?" He observes that, whereas...

using Verma modules. In Weyl's approach, the construction is based on the Peter–Weyl theorem and an analytic proof of the Weyl character formula. Ultimately...

Hilbert space operators. The Peter–Weyl theorem holds, and a version of the Fourier inversion formula (Plancherel's theorem) follows: if f ∈ L2(G), then f...

(see Nouveaux Essais, IV,2)" (ibid p 421) The principle was stated as a theorem of propositional logic by Russell and Whitehead in Principia Mathematica...

(e^{X})},} where W is the Weyl group W = N U ( T ) / T {\displaystyle W=N_{U}(T)/T} and δ(eX) is given by a product formula (Weyl's denominator formula) which...

The Ehrenfest theorem, named after Austrian theoretical physicist Paul Ehrenfest, relates the time derivative of the expectation values of the position...