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Longer titles found: Semisimple Lie algebra (view), Representation theory of semisimple Lie algebras (view)

searching for Simple Lie algebra 20 found (100 total)

Lie algebra bundle (549 words) [view diff] exact match in snippet view article find links to article

bundle is isomorphic to the given Lie algebra bundle. Every semi simple Lie algebra bundle is locally trivial. Hence there exist a Hausdorff Lie group

Principal subalgebra (80 words) [view diff] exact match in snippet view article find links to article

complex simple Lie algebra is a 3-dimensional simple subalgebra whose non-zero elements are regular. A finite-dimensional complex simple Lie algebra has a

Jacobson–Morozov theorem (666 words) [view diff] exact match in snippet view article find links to article

Jacobson–Morozov theorem is the assertion that nilpotent elements in a semi-simple Lie algebra can be extended to sl2-triples. The theorem is named after Jacobson

Dynkin index (270 words) [view diff] exact match in snippet view article find links to article

of finite-dimensional highest-weight representations of a compact simple Lie algebra g {\displaystyle {\mathfrak {g}}} relates their trace forms via Tr

Alvis–Curtis duality (518 words) [view diff] exact match in snippet view article find links to article

transforms of nilpotently supported invariant functions on a finite simple Lie algebra", Japan Academy. Proceedings. Series A. Mathematical Sciences, 57

Rimhak Ree (1,386 words) [view diff] exact match in snippet view article find links to article

Ree, Rimhak (1960), "A family of simple groups associated with the simple Lie algebra of type (G2)", Bulletin of the American Mathematical Society, 66:

Ree group (2,067 words) [view diff] exact match in snippet view article find links to article

Ree, Rimhak (1960), "A family of simple groups associated with the simple Lie algebra of type (G2)", Bulletin of the American Mathematical Society, 66 (6):

Tits group (675 words) [view diff] exact match in snippet view article find links to article

Ree, Rimhak (1961), "A family of simple groups associated with the simple Lie algebra of type (F4)", Bulletin of the American Mathematical Society, 67:

27 (number) (730 words) [view diff] exact match in snippet view article

"Sequence A121737 (Dimensions of the irreducible representations of the simple Lie algebra of type E6 over the complex numbers, listed in increasing order.)"

Gaudin model (2,130 words) [view diff] exact match in snippet view article find links to article

special linear group. Let g {\displaystyle {\mathfrak {g}}} be a semi-simple Lie algebra of finite dimension d {\displaystyle d} . Let N {\displaystyle N}

Iwasawa decomposition (990 words) [view diff] exact match in snippet view article find links to article

{\displaystyle F} . Lie group decompositions Root system of a semi-simple Lie algebra Iwasawa, Kenkichi (1949). "On Some Types of Topological Groups". Annals

Marguerite Frank (467 words) [view diff] case mismatch in snippet view article find links to article

456–482. doi:10.2307/1994156. JSTOR 1994156. Frank, M. (1973). "A New Simple Lie Algebra of Characteristic Three". Proceedings of the American Mathematical

Knizhnik–Zamolodchikov equations (3,059 words) [view diff] exact match in snippet view article find links to article

{\displaystyle B_{n}} introduced by Emil Artin. In general, A complex semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} and its representations ( ρ , V

Outer automorphism group (1,123 words) [view diff] exact match in snippet view article find links to article

diagram follows from the general fact, that for a complex or real simple Lie algebra, 𝔤, the automorphism group Aut(𝔤) is a semidirect product of Inn(𝔤)

En (Lie algebra) (1,481 words) [view diff] exact match in snippet view article

Deligne, Cohen and de Man. E7+1⁄2 has dimension 190, but is not a simple Lie algebra: it contains a 57 dimensional Heisenberg algebra as its nilradical

1960 in science (2,143 words) [view diff] exact match in snippet view article find links to article

Ree, Rimhak (1960). "A family of simple groups associated with the simple Lie algebra of type (G2)". Bulletin of the American Mathematical Society. 66 (6):

Vertex operator algebra (8,906 words) [view diff] exact match in snippet view article find links to article

universal central extension of the loop algebra on a finite-dimensional simple Lie algebra), one may construct the vacuum representation in much the same way

Spin chain (1,138 words) [view diff] exact match in snippet view article find links to article

Lie algebra can be taken to be any complex, finite-dimensional semi-simple Lie algebra g {\displaystyle {\mathfrak {g}}} . More generally still it can be

Alexander Varchenko (2,033 words) [view diff] exact match in snippet view article find links to article

group S n + 1 {\displaystyle S_{n+1}} which is the Weyl group of the simple Lie algebra of type A n {\displaystyle A_{n}} . In 1971, Varchenko proved that

Canonical basis (2,579 words) [view diff] exact match in snippet view article find links to article

canonical basis for the irreducible representations of the corresponding simple Lie algebra, which was not known earlier. Specializing the parameter q {\displaystyle