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searching for Lie algebra 48 found (915 total)

alternate case: lie algebra

Representation theory of SL2(R) (1,827 words) [view diff] exact match in snippet view article

basis H, X, Y for the complexification of the Lie algebra of SL(2, R) so that iH generates the Lie algebra of a compact Cartan subgroup K (so in particular

Nottingham group (327 words) [view diff] no match in snippet view article find links to article

In the mathematical field of infinite group theory, the Nottingham group is the group J(Fp) or N(Fp) consisting of formal power series t + a2t2+... with

Vector-valued differential form (2,332 words) [view diff] exact match in snippet view article find links to article

differential forms. An important case of vector-valued differential forms are Lie algebra-valued forms. (A connection form is an example of such a form.) Let M

Noncommutative symmetric function (354 words) [view diff] exact match in snippet view article find links to article

isomorphic as a Hopf algebra to the universal enveloping algebra of the free Lie algebra on countably many variables. The underlying algebra of the Hopf algebra

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

from a subalgebra of the universal enveloping algebra of a semisimple Lie algebra to the universal enveloping algebra of a subalgebra. A particularly important

Siegel domain (1,069 words) [view diff] exact match in snippet view article find links to article

then L⊆K A j-algebra is a Lie algebra G with a subalgebra K and a linear map j satisfying the properties above. The Lie algebra of a connected Lie group

Mutation (Jordan algebra) (15,817 words) [view diff] exact match in snippet view article

the corresponding complex Lie algebra contains the operators L(a). The commutators [L(a),L(b)] span the complex Lie algebra of derivations of A. The operators

Bispinor (3,655 words) [view diff] exact match in snippet view article find links to article

The basis elements of so(3,1) are labeled Mμν. A representation of the Lie algebra so(3,1) of the Lorentz group O(3,1) will emerge among matrices that will

Harish-Chandra's regularity theorem (957 words) [view diff] exact match in snippet view article find links to article

group G or its Lie algebra is called invariant if it is invariant under conjugation by G. A distribution on a group G or its Lie algebra is called an eigendistribution

Integrable module (104 words) [view diff] exact match in snippet view article find links to article

algebra g {\displaystyle {\mathfrak {g}}} (a certain infinite-dimensional Lie algebra) is a representation of g {\displaystyle {\mathfrak {g}}} such that (1)

Albert algebra (717 words) [view diff] exact match in snippet view article find links to article

Kantor–Koecher–Tits construction applied to an Albert algebra gives a form of the E7 Lie algebra. The split Albert algebra is used in a construction of a 56-dimensional

Convenient vector space (4,011 words) [view diff] exact match in snippet view article find links to article

connected smooth Lie group modeled on convenient vector spaces, with Lie algebra g = T e G {\displaystyle {\mathfrak {g}}=T_{e}G} . Multiplication and

Convenient vector space (4,011 words) [view diff] exact match in snippet view article find links to article

connected smooth Lie group modeled on convenient vector spaces, with Lie algebra g = T e G {\displaystyle {\mathfrak {g}}=T_{e}G} . Multiplication and

Paravector (4,422 words) [view diff] exact match in snippet view article find links to article

(n)} Lie algebra. The bivectors of the three-dimensional Euclidean space form the s p i n ( 3 ) {\displaystyle \mathrm {spin} (3)} Lie algebra, which

Equivariant differential form (439 words) [view diff] exact match in snippet view article find links to article

) {\displaystyle \alpha :{\mathfrak {g}}\to \Omega ^{*}(M)} from the Lie algebra g = Lie ⁡ ( G ) {\displaystyle {\mathfrak {g}}=\operatorname {Lie} (G)}

Eric M. Opdam (240 words) [view diff] exact match in snippet view article find links to article

Iwahori–Hecke algebras, with hypergeometric functions associated with Lie algebra root systems (Heckman-Opdam hypergeometric functions), and with Dunkl

Hamiltonian lattice gauge theory (257 words) [view diff] exact match in snippet view article find links to article

U(e) is the electric field E(e) whose eigenvalues take on values in the Lie algebra g {\displaystyle {\mathfrak {g}}} . The Hamiltonian receives contributions

Blattner's conjecture (890 words) [view diff] exact match in snippet view article find links to article

classification of irreducible Harish-Chandra modules of any real semisimple Lie algebra. Enright, Thomas J; Varadarajan, V. S. (1975), "On an infinitesimal characterization

Rotation matrix (15,724 words) [view diff] exact match in snippet view article find links to article

representation theory of compact semi-simple groups is ready for use. The Lie algebra so(n) of SO(n) is given by s o ( n ) = o ( n ) = { X ∈ M n ( R ) ∣ X

Lang's theorem (808 words) [view diff] exact match in snippet view article find links to article

any σ {\displaystyle \sigma } that induces a nilpotent operator on the Lie algebra of G. Steinberg (1968) gave a useful improvement to the theorem. Suppose

't Hooft symbol (1,248 words) [view diff] exact match in snippet view article find links to article

collection of numbers which allows one to express the generators of the SU(2) Lie algebra in terms of the generators of Lorentz algebra. The symbol is a blend

Glossary of string theory (5,167 words) [view diff] exact match in snippet view article find links to article

exceptional Lie algebra of rank 6 and dimension 78. E7 E7 the exceptional Lie algebra of rank 7 and dimension 133. E8 E8 the exceptional Lie algebra of rank

Gaugino condensation (341 words) [view diff] exact match in snippet view article find links to article

and Λ {\displaystyle \Lambda } is an energy scale, a and b represent Lie algebra indices and α and β represent van der Waerden (two component spinor)

Exterior algebra (12,118 words) [view diff] exact match in snippet view article find links to article

n} ⁠-fold product of exterior algebras. Let L {\displaystyle L} be a Lie algebra over a field ⁠ K {\displaystyle K} ⁠, then it is possible to define the

Exterior covariant derivative (2,816 words) [view diff] exact match in snippet view article find links to article

=d\phi +\rho (\omega )\cdot \phi ,} where, following the notation in Lie algebra-valued differential form § Operations, we wrote ( ρ ( ω ) ⋅ ϕ ) ( v 1

Adjoint (194 words) [view diff] exact match in snippet view article find links to article

a linear operator) in functional analysis Adjoint endomorphism of a Lie algebra Adjoint representation of a Lie group Adjoint functors in category theory

Localization formula for equivariant cohomology (541 words) [view diff] exact match in snippet view article find links to article

torus action and for a sufficient small ξ {\displaystyle \xi } in the Lie algebra of the torus T, we have 1 d M ∫ M α ( ξ ) = ∑ F 1 d F ∫ F α ( ξ ) e T

Ehresmann connection (3,155 words) [view diff] exact match in snippet view article find links to article

adjoint representation of G on its Lie algebra. It maps vertical vector fields to their associated elements of the Lie algebra: ω(X)=ι(X) for all X∈V. Conversely

Dempwolff group (594 words) [view diff] exact match in snippet view article find links to article

{\displaystyle E_{8}} as the subgroup fixing a certain lattice in the Lie algebra of E 8 {\displaystyle E_{8}} , and is also contained in the Thompson

Thompson sporadic group (505 words) [view diff] exact match in snippet view article find links to article

as the automorphism group of a certain lattice in the 248-dimensional Lie algebra of E8. It does not preserve the Lie bracket of this lattice, but does

Lattice (discrete subgroup) (4,840 words) [view diff] exact match in snippet view article

Lie group N {\displaystyle N} contains a lattice if and only if the Lie algebra n {\displaystyle {\mathfrak {n}}} of N {\displaystyle N} can be defined

Dmitry Fuchs (687 words) [view diff] exact match in snippet view article find links to article

Genealogy Project Israel M. Gel'fand, Dmitry B. Fuks: Cohomologies of Lie algebra of tangential vector fields of a smooth manifold. In: Functional Analysis

Demazure module (820 words) [view diff] exact match in snippet view article find links to article

called a Demazure polynomial. Suppose that g is a complex semisimple Lie algebra, with a Borel subalgebra b containing a Cartan subalgebra h. An irreducible

Fuzzy sphere (582 words) [view diff] exact match in snippet view article find links to article

form a basis for the j dimensional irreducible representation of the Lie algebra su(2). They satisfy the relations [ J a , J b ] = i ϵ a b c J c {\displaystyle

Rapidity (2,057 words) [view diff] exact match in snippet view article find links to article

one-dimensional Lie algebra spanned by the anti-diagonal unit matrix, showing that the rapidity is the coordinate on this Lie algebra. In matrix exponential

Representation up to homotopy (1,151 words) [view diff] exact match in snippet view article find links to article

differential geometry, it generalizes the notion of representation of a Lie algebra to Lie algebroids and nontrivial vector bundles. As such, it was introduced

Courant algebroid (1,583 words) [view diff] exact match in snippet view article find links to article

d} . Another example of a Courant algebroid is a quadratic Lie algebra, i.e. a Lie algebra with an invariant scalar product. Here the base manifold is

General covariant transformations (784 words) [view diff] exact match in snippet view article find links to article

vector fields on Y {\displaystyle Y} , but this monomorphisms is not a Lie algebra morphism, unless Γ {\displaystyle \Gamma } is flat. However, there is

Maximal compact subgroup (1,772 words) [view diff] exact match in snippet view article find links to article

Neeb (2012). Let g {\displaystyle {\mathfrak {g}}} be a real semisimple Lie algebra with Cartan involution σ. Thus the fixed point subgroup of σ is the maximal

Igor Dmitrievich Ado (458 words) [view diff] exact match in snippet view article find links to article

result which is now known as Ado's Theorem: every finite-dimensional Lie algebra over a field of characteristic zero has a faithful finite-dimensional

Hitchin's equations (1,350 words) [view diff] exact match in snippet view article find links to article

complexification g ⊗ C {\displaystyle {\mathfrak {g}}\otimes \mathbb {C} } of the Lie algebra g {\displaystyle {\mathfrak {g}}} of G {\displaystyle G} . That is, Φ

Curl (mathematics) (5,050 words) [view diff] exact match in snippet view article

identifying bivectors (2-vectors) in 3 dimensions with the special orthogonal Lie algebra s o ( 3 ) {\displaystyle {\mathfrak {so}}(3)} of infinitesimal rotations

Borel–Weil–Bott theorem (1,898 words) [view diff] exact match in snippet view article find links to article

symmetric power. We even have a unified description of the action of the Lie algebra, derived from its realization as vector fields on the Riemann sphere:

Nolan Wallach (1,055 words) [view diff] exact match in snippet view article find links to article

with A. Rocha-Caridi: Characters of irreducible representations of the Lie algebra of vector fields on the circle, Invent. Math., vol. 72, 1983, pp. 57–75

Infinitesimal generator (81 words) [view diff] exact match in snippet view article find links to article

mathematics, the term infinitesimal generator may refer to: an element of the Lie algebra, associated to a Lie group Infinitesimal generator (stochastic processes)

Local rigidity (1,049 words) [view diff] exact match in snippet view article find links to article

_{2}(\mathbb {C} )} and Γ {\displaystyle \Gamma } (this means that its Lie algebra is not that of one of these two groups). There exists a neighbourhood

SU (551 words) [view diff] exact match in snippet view article find links to article

term used in algebra, SU(n) the corresponding Special unitary group § Lie algebra, s u ( n ) {\displaystyle {\mathfrak {su}}(n)} Vought SU, a US Navy Scout

Toral (86 words) [view diff] exact match in snippet view article find links to article

the codename for British presence within Afghanistan post-2014 Toral Lie algebra Surrender of General Toral, an 1898 film Toral de los Guzmanes, a municipality