scholarly journals The structure of the automorphism group of an injective factor and the cocycle conjugacy of discrete abelian group actions

1992 ◽  
Vol 169 (0) ◽  
pp. 105-130 ◽  
Author(s):  
Y. Kawahigashi ◽  
C. E. Sutherland ◽  
M. Takesaki
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Group Actions ◽  
Injective Factor ◽  
Cocycle Conjugacy ◽  
Abelian Group Actions ◽  
Discrete Abelian Group

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

scholarly journals On abelian group actions with TNI-centralizers

2019 ◽  
Vol 47 (7) ◽  
pp. 3003-3006
Author(s):  
Gülin Ercan ◽  
İsmail Ş. Güloğlu
Keyword(s):  
Abelian Group ◽  
Group Actions ◽  
Abelian Group Actions

scholarly journals Local Weyl modules for equivariant map algebras with free abelian group actions

2012 ◽  
Vol 350 (1) ◽  
pp. 386-404 ◽  
Author(s):  
Ghislain Fourier ◽  
Tanusree Khandai ◽  
Deniz Kus ◽  
Alistair Savage
Keyword(s):  
Abelian Group ◽  
Free Abelian Group ◽  
Group Actions ◽  
Weyl Modules ◽  
Equivariant Map ◽  
Abelian Group Actions
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