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

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.

scholarly journals Small Degree Representations of Finite Chevalley Groups in Defining Characteristic

2001 ◽  
Vol 4 ◽  
pp. 135-169 ◽  
Author(s):  
Frank Lübeck
Keyword(s):  
Algebraic Groups ◽  
Small Degree ◽  
Irreducible Representations ◽  
Simple Groups ◽  
Finite Simple Groups ◽  
Linear Algebraic Groups ◽  
Large Rank ◽  
Projective Representations ◽  
Computer Calculations ◽  
Simply Connected

AbstractThe author has determined, for all simple simply connected reductive linear algebraic groups defined over a finite field, all the irreducible representations in their defining characteristic of degree below some bound. These also give the small degree projective representations in defining characteristic for the corresponding finite simple groups. For large rank l, this bound is proportional to l3, and for rank less than or equal to 11 much higher. The small rank cases are based on extensive computer calculations.

Double groups and projective representations

1979 ◽  
Vol 38 (2) ◽  
pp. 489-511 ◽  
Author(s):  
S.L. Altmann
Keyword(s):  
Projective Representations

scholarly journals On projective characters of the same degree

1998 ◽  
Vol 40 (3) ◽  
pp. 431-434 ◽  
Author(s):  
R. J. Higgs
Keyword(s):  
Complex Numbers ◽  
Central Type ◽  
Projective Representations

All groups G considered in this paper are finite and all representations of G are defined over the field of complex numbers. The reader unfamiliar with projective representations is referred to [9] for basic definitions and elementary results. Let Proj (G, α) denote the set of irreducible projective characters of a group G with cocyle α. In previous papers (for exampe [2], [4], and [6]) numerous authors have considered the situation when Proj(G, α) = 1 or 2; such groups are said to be of α-central type or of 2α-central type, respectively. In particular in [4, Theorem A] the author showed that if Proj(G, α) = {ξ1, ξ2}, then ξ1(1)=ξ2(1). This result has recently been independently confirmed in [8, Corollary C].

scholarly journals THE LOGIC BEHIND FEYNMAN'S PATHS

2011 ◽  
Vol 20 (05) ◽  
pp. 893-907
Author(s):  
EDGARDO T. GARCÍA ÁLVAREZ
Keyword(s):  
Quantum Theory ◽  
Probability Distribution ◽  
Trace Formula ◽  
Classical Trajectory ◽  
Quantum Process ◽  
Level Ii ◽  
Feynman Rules ◽  
Projective Representations ◽  
History Of

The classical notions of continuity and mechanical causality are left in order to reformulate the Quantum Theory starting from two principles: (I) the intrinsic randomness of quantum process at microphysical level, (II) the projective representations of symmetries of the system. The second principle determines the geometry and then a new logic for describing the history of events (Feynman's paths) that modifies the rules of classical probabilistic calculus. The notion of classical trajectory is replaced by a history of spontaneous, random and discontinuous events. So the theory is reduced to determining the probability distribution for such histories accordingly with the symmetries of the system. The representation of the logic in terms of amplitudes leads to Feynman rules and, alternatively, its representation in terms of projectors results in the Schwinger trace formula.

The finite inner automorphism groups of division rings

1995 ◽  
Vol 118 (2) ◽  
pp. 207-213 ◽  
Author(s):  
M. Shirvani
Keyword(s):  
Finite Groups ◽  
Galois Theory ◽  
Automorphism Groups ◽  
Outer Automorphism ◽  
Commutative Field ◽  
Division Rings ◽  
Inner Automorphism ◽  
Projective Representations ◽  
Inner Automorphisms ◽  
A Finite Group

Let G be a finite group of automorphisms of an associative ring R. Then the inner automorphisms (x↦ u−1xu = xu, for some unit u of R) contained in G form a normal subgroup G0 of G. In general, the Galois theory associated with the outer automorphism group G/G0 is quit well behaved (e.g. [7], 2·3–2·7, 2·10), while little group-theoretic restriction on the structure of G/G0 may be expected (even when R is a commutative field). The structure of the inner automorphism groups G0 does not seem to have received much attention so far. Here we classify the finite groups of inner automorphisms of division rings, i.e. the finite subgroups of PGL (1, D), where D is a division ring. Such groups also arise in the study of finite collineation groups of projective spaces (via the fundamental theorem of projective geometry, cf. [1], 2·26), and provide examples of finite groups having faithful irreducible projective representations over fields.

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].

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