scholarly journals Projective Representations, Abelian F-Groups, and Central Extensions

1993 ◽  
Vol 160 (1) ◽  
pp. 242-256 ◽  
Author(s):  
E.C. Hwang
Keyword(s):  
Central Extensions ◽  
Projective Representations

Projective representations of rotation subgroups of Weyl groups

1987 ◽  
Vol 101 (1) ◽  
pp. 21-35 ◽  
Author(s):  
D. Theo
Keyword(s):  
Recent Work ◽  
Ad Hoc ◽  
Weyl Groups ◽  
Orthogonal Groups ◽  
Central Extensions ◽  
Projective Representations ◽  
Rotation Groups ◽  
Spin Representations ◽  
Double Coverings

By exploiting the well known spin representations of the orthogonal groups O(l), Morris [12] was able to give a unified construction of some of the projective representations of Weyl groups W(Φ) which had previously only been available by ad hoc means [5]. The principal purpose of the present paper is to give a corresponding construction for projective representations of the rotation subgroups W+(Φ) of Weyl groups. Thus we construct non-trivial central extensions of W+(Φ) via the well-known double coverings of the rotation groups SO(l). This adaptation allows us to give a unified way of obtaining the basic projective representations of W+(Φ) from those of W(Φ) determined in [12]. Hence our work is a development of the recent work of Morris, and is an extension of Schur's work on the alternative groups [15].

Projective Representations of Minimum Degree of Group Extensions

1978 ◽  
Vol 30 (5) ◽  
pp. 1092-1102 ◽  
Author(s):  
Walter Feit ◽  
Jacques Tits
Keyword(s):  
Simple Group ◽  
Central Extension ◽  
Finite Simple Group ◽  
Minimum Degree ◽  
Projective Representation ◽  
Closed Field ◽  
Natural Question ◽  
Central Extensions ◽  
Ordinary Representation ◽  
Projective Representations

Let G be a finite simple group and let F be an algebraically closed field. A faithful projective F-representation of G of smallest possible degree often cannot be lifted to an ordinary representation of G, though it can of course be lifted to an ordinary representation of some central extension of G. It is a natural question to ask whether by considering non-central extensions, it is possible in some cases to decrease the smallest degree of a faithful projective representation.

Existentially closed central extensions of locally finite p-groups

1986 ◽  
Vol 100 (2) ◽  
pp. 281-301 ◽  
Author(s):  
Felix Leinen ◽  
Richard E. Phillips
Keyword(s):  
Central Extensions ◽  
Locally Finite ◽  
Existentially Closed ◽  
Image Position

Throughout, p will be a fixed prime, and will denote the class of all locally finite p-groups. For a fixed Abelian p-group A, we letwhere ζ(P) denotes the centre of P. Notice that A is not a class in the usual group-theoretic sense, since it is not closed under isomorphisms.

scholarly journals Central extensions of 3-dimensional Zinbiel algebras

2021 ◽  
Author(s):  
Ivan Kaygorodov ◽  
María Alejandra Alvarez ◽  
Thiago Castilho de Mello
Keyword(s):  
Central Extensions ◽  
3 Dimensional

scholarly journals On central extensions of preprojective algebras

2007 ◽  
Vol 313 (1) ◽  
pp. 165-175 ◽  
Author(s):  
Pavel Etingof ◽  
Frédéric Latour ◽  
Eric Rains
Keyword(s):  
Central Extensions ◽  
Preprojective Algebras

scholarly journals Projective representations of quivers

2002 ◽  
Vol 31 (2) ◽  
pp. 97-101 ◽  
Author(s):  
Sangwon Park
Keyword(s):  
Projective Representation ◽  
Representations Of Quivers ◽  
Direct Sum ◽  
Projective Representations

We prove thatP1 →f P2is a projective representation of a quiverQ=•→•if and only ifP1andP2are projective leftR-modules,fis an injection, andf (P 1)⊂P 2is a summand. Then, we generalize the result so that a representationM1 →f1  M2  →f2⋯→fn−2  Mn−1→fn−1  Mnof a quiverQ=•→•→•⋯•→•→•is projective representation if and only if eachMiis a projective leftR-module and the representation is a direct sum of projective representations.

Projective representations of SU(2)ΛR4

1979 ◽  
Vol 20 (7) ◽  
pp. 1545-1554 ◽  
Author(s):  
N. B. Backhouse ◽  
J. W. B. Hughes
Keyword(s):  
Projective Representations
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