the group PU(V) is the image of the unitary group U(V) in the automorphism group of the projective space P(V). The projective special unitary group PSU(n)...

and the projective special unitary group PSU(n). These are related as by the commutative diagram at right; notably, both projective groups are equal:...

In projective geometry and linear algebra, the projective orthogonal group PO is the induced action of the orthogonal group of a quadratic space V = (V...

symplectic group, Sp(2n, R), on the phase space. Hamiltonian mechanics Metaplectic group Orthogonal group Paramodular group Projective unitary group Representations...

general linear group of a vector space V on the associated projective space P(V). Explicitly, the projective linear group is the quotient group PGL(V) = GL(V) / Z(V)...

already discussed the irreducible projective unitary representations of the rotation group SO(3) above; considering projective representations allows for fractional...

special unitary group of degree n, denoted SU(n), is the Lie group of n × n unitary matrices with determinant 1. The matrices of the more general unitary group...

group of unitary symplectic matrices, Sp(r) and as its associated centerless group the Lie group PSp(r) = Sp(r)/{I, −I} of projective unitary symplectic...

mathematics, projective group may refer to: Projective linear group or one of the related linear groups Projective orthogonal group Projective unitary group Projective...

complex projective space is the projective space with respect to the field of complex numbers. By analogy, whereas the points of a real projective space...

mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism from G to the projective linear group P G L (...

{\displaystyle \psi } . This is a projective representation, a homomorphism from the symplectic group to the projective unitary group of H {\displaystyle {\mathcal...

projective orthogonal group. PSU – projective special unitary group. PU – projective unitary group. Q – rational numbers. QED – "Quod erat demonstrandum"...

quotients the projective unitary group PUn(R) = Un(R)/Z(Un(R)) and the projective special unitary group PSUn(R) = SUn(R)/Z(SUn(R)) The symplectic group Sp2n(R)...

group M24, the exceptional covers of the projective unitary group U4(3) and the projective special linear group L 3 ( 4 ) , {\displaystyle L_{3}(4),} and...

the classical groups and the groups of exceptional type in a 1955 paper. This omitted certain known groups (the projective unitary groups), which were...

Foundation's Mandate for Leadership series, Project 2025 is based on a controversial interpretation of the unitary executive theory that states that the entire...

linear group with the Galois group of field automorphisms. For example, PΣU is used for the semilinear analogs of the projective special unitary group PSU...

particularly important types of t-designs in quantum mechanics are projective and unitary t-designs. A spherical design is a collection of points on the unit...

{\displaystyle BU(1)=PU(H),} that is, BU(1) is the infinite-dimensional projective unitary group. See that article for additional discussion and properties. For...

usual construction of the unitary group from the general linear group. The unitary group arises as follows: the general linear group over the complex numbers...

Poincaré group. (More generally, it may be a projective representation, which amounts to a representation of the double cover of the group.) In a classical...

group composition law need only hold up to a constant. According to Bargmann's theorem, every projective unitary representation of the Poincaré group...

regardless of the group G {\displaystyle G} , every projective unitary representation of G {\displaystyle G} comes from an ordinary unitary representation...

group in the projective unitary group PU(1, n). Pierre Deligne and George Mostow used his ideas to construct lattices in the projective unitary group...

In American law, the unitary executive theory is a constitutional law theory according to which the president of the United States has sole authority...

space and the set of projective rays may be treated as a complex projective space; it is a homogeneous space for a unitary group U ( n ) {\displaystyle...

The European patent with unitary effect, also known as the unitary patent, is a European patent which benefits from unitary effect in the participating...

the projective special unitary groups PSU3(2n) for n≥2 the Suzuki groups Sz(22n+1) for n≥1 The C-groups include as special cases the CIT-groups, that...

+ 1 dimensions. We are interested in projective representations of this group, which are equivalent to unitary representations of the nontrivial central...