In the field of representation theory in mathematics, a projective representation of a group G on a vector space V over a field F is a group homomorphism...

concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity. A projective space may thus...

especially in the group theoretic area of algebra, the projective linear group (also known as the projective general linear group or PGL) is the induced action...

isometry group of complex projective space, just as the projective orthogonal group is the isometry group of real projective space. In terms of matrices...

U(\mathbf {H} )} —but rather in projective unitary representations—that is, homomorphisms of G {\displaystyle G} into the projective unitary group P U ( H ) :=...

image and represents entangled states. Complex projective space Projective representation Projective space, for the concept in general Miranda 1995,...

linear representation in dimension n. This reduction depends on a group cohomology question, in general. Group action Projective representation Remm, Elisabeth;...

almost simple groups. The representation theory of the quasisimple groups is nearly identical to the projective representation theory of the simple groups...

typically a representation of the Poincaré group. (More generally, it may be a projective representation, which amounts to a representation of the double...

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...

real projective plane, denoted ⁠ R P 2 {\displaystyle \mathbf {RP} ^{2}} ⁠ or ⁠ P 2 {\displaystyle \mathbb {P} _{2}} ⁠, is a two-dimensional projective space...

the projective general linear group PGL ⁡ ( n , C ) {\displaystyle \operatorname {PGL} (n,\mathbb {C} )} . In other words, a projective representation is...

the representation of a symmetry group on ray space can be lifted to a projective representation or sometimes even an ordinary representation on Hilbert...

the complex projective plane, and finite, such as the Fano plane. A projective plane is a 2-dimensional projective space. Not all projective planes can...

standard representation. For the Lorentz group, the (m, n)-representation is projective when m + n is a half-integer. See § Spinors. For a projective representation...

not projective modules. By contrast, in the characteristic 0 case every irreducible representation is a direct summand of the regular representation, hence...

theorem tells us that every projective unitary representation of G {\displaystyle G} comes from an ordinary representation of the universal cover G ~ {\displaystyle...

the property of lifting that carries over from free to projective modules: a module P is projective if and only if for every surjective module homomorphism...

Bargmann's theorem, every projective unitary representation of the Poincaré group comes from an ordinary unitary representation of its universal cover,...

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

quaternion). This representation can also be viewed as a double-valued projective representation of the rotation group SO(3). The representation with m = 2 {\displaystyle...

double-valued projective representation of the rotation group SO(3). Although spinors can be defined purely as elements of a representation space of the...

is essentially the only projective invariant of a quadruple of collinear points; this underlies its importance for projective geometry. The cross-ratio...

In psychology, a projective test is a personality test designed to let a person respond to ambiguous stimuli, presumably revealing hidden emotions and...

Newsom. She is the director, writer, and producer of the film Miss Representation (2011), which premiered in the documentary competition at the Sundance...

not observable, then a projective representation reduces to an ordinary representation. All representations are also projective representations, but the...

immediately give a representation of SL 2 ( Z ) {\displaystyle {\text{SL}}_{2}(\mathbb {Z} )} - they only give a projective representation. This can be fixed...

the theory of projective representations, in cases where the projective representation cannot be lifted to an ordinary linear representation. In the case...

amplitude. In mathematical terms, the quantum Hilbert space carries a projective representation of the rotation group SO(3). Suppose a detector that can be rotated...

bundles to the algebraic concept of projective modules, and for the Swan representation, an l-adic projective representation of a Galois group. His work has...