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searching for Cartan subalgebra 15 found (117 total)

alternate case: cartan subalgebra

Harish-Chandra homomorphism (163 words) [view diff] exact match in snippet view article find links to article

universal enveloping algebra with the invariant polynomials on a Cartan subalgebra. In the case of the K-invariant elements of the universal enveloping
Harish-Chandra's regularity theorem (947 words) [view diff] exact match in snippet view article find links to article
finite-dimensional. The regularity theorem also implies that on each Cartan subalgebra the distribution can be written as a finite sum of exponentials divided
Manin triple (354 words) [view diff] exact match in snippet view article find links to article
of elements (x,y) with x in a fixed Borel subalgebra containing a Cartan subalgebra h, y in the opposite Borel subalgebra, and where x and y have the
Quantum group (4,637 words) [view diff] exact match in snippet view article find links to article
t_{\lambda }} and tλ is the element of the Cartan subalgebra satisfying (tλ, h) = λ(h) for all h in the Cartan subalgebra. There are various coassociative coproducts
An Exceptionally Simple Theory of Everything (2,347 words) [view diff] exact match in snippet view article find links to article
collection of R mutually-commuting Lie algebra generators, spanning a Cartan subalgebra. Each elementary particle state can be thought of as a different orthogonal
Weight (representation theory) (3,204 words) [view diff] exact match in snippet view article
complex semisimple Lie algebra and h{\displaystyle {\mathfrak {h}}} a Cartan subalgebra of g{\displaystyle {\mathfrak {g}}}. In this section, we describe
Lie bialgebra (931 words) [view diff] exact match in snippet view article find links to article
compatible Lie algebra structure on the dual vector space. Choose a Cartan subalgebra t⊂g{\displaystyle {\mathfrak {t}}\subset {\mathfrak {g}}} and a choice
Glossary of representation theory (5,008 words) [view diff] exact match in snippet view article find links to article
complex semisimple Lie algebra g {\displaystyle {\mathfrak {g}}} , Cartan subalgebra h {\displaystyle {\mathfrak {h}}} and a choice of a positive Weyl
Automorphism of a Lie algebra (714 words) [view diff] exact match in snippet view article find links to article
{\displaystyle {\mathfrak {g}}} can be mapped to a subalgebra of a Cartan subalgebra h {\displaystyle {\mathfrak {h}}} of g {\displaystyle {\mathfrak {g}}}
't Hooft loop (1,854 words) [view diff] exact match in snippet view article find links to article
line can always be written in terms of the rank r{\displaystyle r} Cartan subalgebra H{\displaystyle {\boldsymbol {H}}} as Q=m⋅H{\displaystyle Q={\boldsymbol
Serre's theorem on a semisimple Lie algebra (1,340 words) [view diff] exact match in snippet view article find links to article
i\neq j} . is a finite-dimensional semisimple Lie algebra with the Cartan subalgebra generated by h i {\displaystyle h_{i}} 's and with the root system
Character theory (3,416 words) [view diff] exact match in snippet view article find links to article
g{\displaystyle {\mathfrak {g}}} is a complex semisimple Lie algebra with Cartan subalgebra h{\displaystyle {\mathfrak {h}}}. The value of the character χρ{\displaystyle
Weyl's theorem on complete reducibility (2,447 words) [view diff] exact match in snippet view article find links to article
{\mathfrak {g}}} be the Borel subalgebra determined by a choice of a Cartan subalgebra and positive roots. Let V 0 = { v ∈ V | n + ( v ) = 0 } {\displaystyle
Compact group (4,392 words) [view diff] exact match in snippet view article find links to article
maximal torus in a compact group plays a role analogous to that of the Cartan subalgebra in a complex semisimple Lie algebra. In particular, once a maximal
Classification of finite simple groups (3,909 words) [view diff] exact match in snippet view article find links to article
2-subgroup, which is often (but not always) the same as the rank of a Cartan subalgebra when the group is a group of Lie type in characteristic 2. The rank