scholarly journals The exponent and the projective representations of a finite group

1967 ◽  
Vol 11 (3) ◽  
pp. 410-413 ◽  
Author(s):  
J. L. Alperin ◽  
Tzee-Nan Kuo
Keyword(s):  
Finite Group ◽  
Projective Representations ◽  
A Finite Group

scholarly journals THE DUAL STRUCTURE OF CROSSED PRODUCT -ALGEBRAS WITH FINITE GROUPS

2013 ◽  
Vol 88 (2) ◽  
pp. 243-249 ◽  
Author(s):  
FIRUZ KAMALOV
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Orbit Space ◽  
Crossed Product ◽  
Irreducible Representations ◽  
Natural Action ◽  
Dual Structure ◽  
Projective Representations ◽  
A Finite Group ◽  
Sigma G

AbstractWe study the space of irreducible representations of a crossed product ${C}^{\ast } $-algebra ${\mathop{A\rtimes }\nolimits}_{\sigma } G$, where $G$ is a finite group. We construct a space $\widetilde {\Gamma } $ which consists of pairs of irreducible representations of $A$ and irreducible projective representations of subgroups of $G$. We show that there is a natural action of $G$ on $\widetilde {\Gamma } $ and that the orbit space $G\setminus \widetilde {\Gamma } $ corresponds bijectively to the dual of ${\mathop{A\rtimes }\nolimits}_{\sigma } G$.

scholarly journals Projective representations of extra-special p-groups

1978 ◽  
Vol 19 (2) ◽  
pp. 149-152 ◽  
Author(s):  
Hans Opolka
Keyword(s):  
Finite Group ◽  
Characteristic Zero ◽  
Cohomology Group ◽  
Multiplicative Group ◽  
Neutral Element ◽  
Closed Field ◽  
Algebra Isomorphism ◽  
Twisted Group Algebra ◽  
Projective Representations ◽  
A Finite Group

Let G be a finite group (with neutral element e) which operates trivially on the multiplicative group R* of a commutative ring R (with identity 1). Let H2(G, R*) denote the second cohomology group of G with respect to the trivial G-module R*. With every represented by the central factor system we associate the so called twisted group algebra (R, G, f) (see [3, V, 23.7] for the definition). (R, G, f) is determined by f up to R-algebra isomorphism. In this note we shall describe its representations in the case R is an algebraically closed field C of characteristic zero and G is an extra-special p-group P.

scholarly journals On tensor factorisation for representations of finite groups

2004 ◽  
Vol 69 (1) ◽  
pp. 161-171 ◽  
Author(s):  
Emanuele Pacifici
Keyword(s):  
Finite Group ◽  
Tensor Product ◽  
Finite Groups ◽  
Group Structure ◽  
Complex Representation ◽  
Normal Subgroups ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

We prove that, given a quasi-primitive complex representation D for a finite group G, the possible ways of decomposing D as an inner tensor product of two projective representations of G are parametrised in terms of the group structure of G. More explicitly, we construct a bijection between the set of such decompositions and a particular interval in the lattice of normal subgroups of G.

Real projective representations of finite groups

1990 ◽  
Vol 107 (1) ◽  
pp. 27-32 ◽  
Author(s):  
P. N. Hoffmann ◽  
J. F. Humphreys
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Schur Multiplier ◽  
Representations Of Finite Groups ◽  
Projective Representations ◽  
A Finite Group

The projective representations of a finite group G over a field K are divided into sets, each parametrized by an element of the group H2(G, Kx). The latter is the Schur multiplier M(G) when K = ℂ.

scholarly journals Groups whose Projective character degrees are powers of a prime

1988 ◽  
Vol 30 (2) ◽  
pp. 177-180 ◽  
Author(s):  
R. J. Higgs
Keyword(s):  
Finite Group ◽  
Projective Representation ◽  
Character Degrees ◽  
Projective Character ◽  
Projective Representations ◽  
A Finite Group

Let Gbe a finite group, and P:G → GL(n, ) be such that for all x, y ∈ G(i) P(x)P(y) = α(x, y)P(xy), and(ii)P(l) = In,where α(x, y) ∈ *; then P is a projective representation of G with cocycle α and degree n. For other basic definitions concerning projective representations see [4].

Simple objects in equivariantized module categories

2019 ◽  
Vol 18 (01) ◽  
pp. 1950001
Author(s):  
Sara Pinter ◽  
Virgínia Rodrigues
Keyword(s):  
Finite Group ◽  
Direct Summand ◽  
Indecomposable Module ◽  
Simple Object ◽  
Fusion Category ◽  
Module Category ◽  
Bijective Correspondence ◽  
Isomorphism Classes ◽  
Projective Representations ◽  
A Finite Group

Let [Formula: see text] be a finite group acting on a fusion category [Formula: see text] and let [Formula: see text] be a subgroup of [Formula: see text]. Let [Formula: see text] be a semisimple indecomposable module category over [Formula: see text]. Considering [Formula: see text] a simple object in [Formula: see text] and [Formula: see text] the stabilizer (or inertia) subgroup of [Formula: see text], we establish a bijective correspondence between isomorphism classes of simple objects in equivariantizations [Formula: see text] and [Formula: see text], where such simple objects contain [Formula: see text] as a direct summand. Also, as an application to projective representations of [Formula: see text], we relate isomorphism classes of simple objects in [Formula: see text] with irreducible projective representations of [Formula: see text].

ON HIGHER FROBENIUS–SCHUR INDICATORS

2021 ◽  
pp. 1-11
Author(s):  
YANJUN LIU ◽  
WOLFGANG WILLEMS
Keyword(s):  
Finite Group ◽  
Representation Theory ◽  
Irreducible Characters ◽  
A Finite Group

Abstract Similarly to the Frobenius–Schur indicator of irreducible characters, we consider higher Frobenius–Schur indicators $\nu _{p^n}(\chi ) = |G|^{-1} \sum _{g \in G} \chi (g^{p^n})$ for primes p and $n \in \mathbb {N}$ , where G is a finite group and $\chi $ is a generalised character of G. These invariants give answers to interesting questions in representation theory. In particular, we give several characterisations of groups via higher Frobenius–Schur indicators.

scholarly journals Finite groups with some weakly pronormal subgroups

2020 ◽  
Vol 18 (1) ◽  
pp. 1742-1747
Author(s):  
Jianjun Liu ◽  
Mengling Jiang ◽  
Guiyun Chen
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
A Finite Group

Abstract A subgroup H of a finite group G is called weakly pronormal in G if there exists a subgroup K of G such that G = H K G=HK and H ∩ K H\cap K is pronormal in G. In this paper, we investigate the structure of the finite groups in which some subgroups are weakly pronormal. Our results improve and generalize many known results.

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