projective representation

Projective representation · 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 ...

Why should I care about projective representations in quantum theory?

Wigner's theorem tells us that the correct thing to do is to seek a projective unitary or antiunitary representation of G on H, which descends ...

Projective representations of groups - Alistair Savage

projective representation, group, symmetric group, central extension, group cohomology. Page 2. 2. EDUARDO MONTEIRO MENDONCA the first to realize that, for ...

Projective and spin representations - University of Alberta

Roughly speaking, spin representations are representations of the elements of SO(n) S O ( n ) (which you can think of as rotations) that pick a sign when you ...

projective representation in nLab

1. Definition. A projective representation of a group G G is a representation up to a central term: a group homomorphism G ⟶ PGL ( V ) G\ ...

Computing characters of α-projective representations - MathOverflow

Computing characters of α-projective representations ... Given a finite group G, a finite cyclic group A (viewed as a subgroup of C×, i.e. ...

Projective representation - Groupprops - subwiki.org

2.3When is a projective representation equivalent to a linear representation? Projective representation.

Projective representations and group cohomology

The projective representations are the maps θ:G→PGL(V), not the lifts. For each θ there is a unique cohomology class [α]∈H2(BG,C∗) since, ...

Review of Projective Representations of Finite Groups

Projective representations take their name from projective geometry. To be specific, let G be a finite group, K a field, and V a finite-dimensional.

A character theory for projective representations of finite groups

A projective representation ( π , V , α ) of G over C is a continuous map π : G → U ( V ) such that π ( x ) π ( y ) = α ( x , y ) π ( x y ) for ...

Projective unitary group - Wikipedia

Projective special unitary group · Examples · Finite fields · The topology of PU(H) · Representations · Applications · References · See also.

character theory for projective representations of finite groups

Theorem 2.3. Every projective representation of G is a direct sum of irreducible projective representations. Proof. Let V be a projective representation of G.

Projective representation theory for compact quantum groups and ...

We show that a projective representation is continuous, i.e. restricts to an action on the compact operators \mathcal{K}(H), if and only if the ...

Projective Representation of Algebraic Linear Groups of ... - jstor

PROJECTIVE REPRESENTATION OF ALGEBRAIC LINEAR. GROUPS OF TRANSFORMATIONS.' By T. KAMBAYASHI. Let g be an algebraic linear group, not necessarily connected ...

Projective Representations

The theory of projective representations was developed by Schur [1–3]. He showed that irreducible projective representations can be obtained by constructing ...

Reference recommendation for Projective representation, group ...

It says that a Lie group can have nontrivial projective represention if the Lie group is not simple connected or the Lie algebra has nontrivial ...

2.4 Z2×Z2 Z 2 × Z 2 projective representation

If the two energy were distinct, each state should consist a one-dimensional representation with the projective phase, which contradicts with the above ...

Induced projective representations | Journal of Mathematical Physics

Induced projective representations ... The left‐ (right‐) regular projective representation of a finite group G and the corresponding ''projective ...

Projective representation of the Galilei group for classical and ... - arXiv

Here we show, by direct construction, that classical mechanics also allows for a projective representation of the Galilei group where the mass ...

Projective representation - Encyclopedia of Mathematics

Projective representations arise naturally in studying linear representations of group extensions. The most important examples of projective ...