group (and also the spin group, a double cover) SL ( 2 , C ) {\displaystyle {\text{SL}}(2,\mathbb {C} )} of SO ( 3 ; 1 ) + {\displaystyle {\text{SO}}(3;1)^{+}}...

form Q, SL(2, C) acts by Lorentz transformations. On dimensional grounds, SL(2, C) covers a neighborhood of the identity of SO(1, 3). Since SL(2, C) is connected...

group SL(2, R) or SL2(R) is the group of 2 × 2 real matrices with determinant one: SL ( 2 , R ) = { ( a b c d ) : a , b , c , d ∈ R  and  a d − b c = 1...

is R or C, SL(n, F) is a Lie subgroup of GL(n, F) of dimension n2 − 1. The Lie algebra s l ( n , F ) {\displaystyle {\mathfrak {sl}}(n,F)} of SL(n, F) consists...

Mercedes-Benz SL-Class (marketed as Mercedes-AMG SL since 2022) is a grand touring sports car manufactured by Mercedes-Benz since 1954. The designation "SL" derives...

group has order 2, and its universal cover, the indefinite spin group Spin(1, 3), is isomorphic to both the special linear group SL(2, C) and to the symplectic...

corresponds to a representation by contraction operators of the semigroup in SL(2,C) corresponding to Möbius transformations that take the unit disk into itself...

S L 2 ( C ) {\displaystyle \mathrm {SL} _{2}(\mathbb {C} )} . A lattice Γ {\displaystyle \Gamma } in S L 2 ( C ) {\displaystyle \mathrm {SL} _{2}(\mathbb...

{H}}^{2}} . As for SL(2,C), this immediately implies the Plancherel formula for fi in Cc(SL(2,R) / SO(2)): ∫ H 2 f 1 f 2 ¯ d A = ∫ − ∞ ∞ f ~ 1 f 2 ~ ¯ λ...

As an example, consider the case g = sl ⁡ ( 2 ; C ) {\displaystyle {\mathfrak {g}}=\operatorname {sl} (2;\mathbb {C} )} discussed above. If the highest...

of sl(3,C) Hall 2015, Section 6.2. (There specialized to sl ⁡ ( 3 , C {\displaystyle \operatorname {sl} (3,\mathbb {C} } ) Hall 2015, Section 7.2. Bäuerle...

studied by Bargmann (1947) for G = SL(2,R) and by Harish-Chandra (1947) and Gelfand & Naimark (1947) for G = SL(2,C). Subsequently in the 1960s, the construction...

is the special linear group. The Lie algebra s l 2 C {\displaystyle {\mathfrak {sl}}_{2}\mathbb {C} } is central to the study of special relativity,...

\Lambda ]=\Pi } . Comparing with the Lie algebra s l ( 2 , C ) {\displaystyle {\mathfrak {sl}}(2,\mathbb {C} )} , one sees that { Π , L , Λ } {\displaystyle...

1/2; i.e. fermions. Here SL ⁡ ( 2 , C ) {\displaystyle \operatorname {SL} (2,\mathbf {C} )} is the group of complex 2 × 2 {\displaystyle 2\times 2} matrices...

called the inhomogeneous SL(2, C); this has elements (a, A), where as before, a is a four-vector, but now A is a complex 2 × 2 matrix with unit determinant...

The R230 generation of the Mercedes-Benz SL-Class was introduced at the 2001 Frankfurt Motor Show and 2001 Bologna Motor Show, replacing the R129. The...

complex plane C. The one-point compactification of C, the Riemann sphere, is the dual space, a homogeneous space for SU(2) and SL(2,C). Irreducible compact...

Stationary Low-Power Reactor Number One, also known as SL-1, initially the Argonne Low Power Reactor (ALPR), was a United States Army experimental nuclear...

( C × I ) ≅ SL 2 ⁡ ( C ) / { ± I } =: PSL 2 ⁡ ( C ) {\displaystyle \operatorname {PGL} _{2}(\mathbb {C} ):=\operatorname {GL} _{2}\left(\mathbb {C} )/(\mathbb...

Representation theory of the Lorentz group. SL ( 2 , C ) ≅ Spin ( 1 , 3 ) {\displaystyle {\text{SL}}(2,\mathbb {C} )\cong {\text{Spin}}(1,3)} : The spin group...

representations of SL(2,C) (the spinors) forms the adjoint rep of the Lorentz group SO(3,1); abstractly, one writes 2 ⊗ 2 ¯ = 3 ⊕ 1.   {\displaystyle 2\otimes {\overline...

See Mercedes-Benz SL-Class for a complete overview of all SL-Class models. The Mercedes-Benz W 113 is a two-seat roadster/coupé, introduced at the 1963...

In computational complexity theory, SL (Symmetric Logspace or Sym-L) is the complexity class of problems log-space reducible to USTCON (undirected s-t...

representation of Q8 in the special linear group SL ⁡ ( 2 , C ) {\displaystyle \operatorname {SL} (2,\mathbb {C} )} . A variant gives a representation by unitary...

subgroups of ⁠ SL ( 2 , C ) , {\displaystyle {\text{SL}}(2,\mathbb {C} ),} ⁠ the canonical representation on ⁠ C 2 {\displaystyle \mathbb {C} ^{2}} ⁠ is self-dual...

they transform according to some representation S of the Lorentz group, or SL(2,C) if the spin is not integer: U ( a , L ) † A ( x ) U ( a , L ) = S ( L )...

SL ( 2 , Z ) = { ( a b c d ) | a , b , c , d ∈ Z ,   a d − b c = 1 } {\displaystyle {\text{SL}}(2,\mathbf {Z} )=\left\{\left.{\begin{pmatrix}a&b\\c...

reduced PVS in terms of semisimple G ≤ SL(V) and n ≥ 1 such that either: (G × SL(n), V ⊗ Fn) is a PVS; (G × SL(n), V ⊗ Fn) is not a PVS, but (G × GL(n)...

in the Lie algebra s l ( 2 ; C ) {\displaystyle {\mathfrak {sl}}(2;\mathbb {C} )} (the space of 2 × 2 {\displaystyle 2\times 2} matrices with trace zero):...