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 (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)^{+}}...

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...

n , C ) {\displaystyle \operatorname {SL} (n,\mathbb {C} )} is also simply connected, for all n ≥ 2 {\displaystyle n\geq 2} . The topology of SL ⁡ ( n...

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...

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...

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

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...

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...

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,...

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...

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...

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...

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

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...

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...

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)...

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...

{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...

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...

( SL ⁡ ( 2 , C ) , Z ) − → P ( H 3 ) → R ⊗ Z R / 2 π Z → H 2 ( SL ⁡ ( 2 , C ) , Z ) − → 0 {\displaystyle 0\to H_{3}(\operatorname {SL} (2,\mathbb {C} )...

special linear group SL ⁡ ( 2 , C ) {\displaystyle \operatorname {SL} (2,\mathbb {C} )} is isomorphic to the symplectic group Sp ⁡ ( 2 , C ) . {\displaystyle...

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

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

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...

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

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...

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 )...

The IRIS-T SL is a family of short and high to medium air defense surface-to-air missile systems. The missile systems are developed from the IRIS-T air-to-air...

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