scholarly journals Ergodic properties of a class of discrete Abelian group extensions of rank-one transformations

2010 ◽  
Vol 119 (1) ◽  
pp. 1-22
Author(s):  
Chris Dodd ◽  
Phakawa Jeasakul ◽  
Anne Jirapattanakul ◽  
Daniel M. Kane ◽  
Becky Robinson ◽  
...  
Keyword(s):  
Abelian Group ◽  
Group Extensions ◽  
Ergodic Properties ◽  
Rank One ◽  
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 A note on central group extensions

1973 ◽  
Vol 15 (4) ◽  
pp. 428-429 ◽  
Author(s):  
G. J. Hauptfleisch
Keyword(s):  
Abelian Group ◽  
Homomorphic Image ◽  
Free Group ◽  
Central Extension ◽  
Dihedral Group ◽  
Group Extension ◽  
Central Group ◽  
Group Extensions

If A, B, H, K are abelian group and φ: A → H and ψ: B → K are epimorphisms, then a given central group extension G of H by K is not necessarily a homomorphic image of a group extension of A by B. Take for instance A = Z(2), B = Z ⊕ Z, H = Z(2), K = V4 (Klein's fourgroup). Then the dihedral group D8 is a central extension of H by K but it is not a homomorphic image of Z ⊕ Z ⊕ Z(2), the only group extension of A by the free group B.

scholarly journals The Spectral Radius Formula for Fourier–Stieltjes Algebras

2019 ◽  
Vol 63 (2) ◽  
pp. 269-275
Author(s):  
Przemysław Ohrysko ◽  
Maria Roginskaya
Keyword(s):  
Abelian Group ◽  
Spectral Radius ◽  
Haar Measure ◽  
Short Note ◽  
Measure Algebra ◽  
Stieltjes Transform ◽  
Locally Compact ◽  
Convolution Powers ◽  
Discrete Abelian Group ◽  
Spectral Radius Formula

AbstractIn this short note we first extend the validity of the spectral radius formula, obtained by M. Anoussis and G. Gatzouras, for Fourier–Stieltjes algebras. The second part is devoted to showing that, for the measure algebra on any locally compact non-discrete Abelian group, there are no non-trivial constraints among three quantities: the norm, the spectral radius, and the supremum of the Fourier–Stieltjes transform, even if we restrict our attention to measures with all convolution powers singular with respect to the Haar measure.

scholarly journals A note on Abelian group extensions

1962 ◽  
Vol 12 (4) ◽  
pp. 1401-1403 ◽  
Author(s):  
Ronald Nunke
Keyword(s):  
Abelian Group ◽  
Group Extensions

The corepresentation ring of a pointed Hopf algebra of rank one

2018 ◽  
Vol 17 (12) ◽  
pp. 1850236
Author(s):  
Zhihua Wang
Keyword(s):  
Abelian Group ◽  
Hopf Algebra ◽  
Nilpotent Element ◽  
Finite Abelian Group ◽  
Generators And Relations ◽  
Direct Sum ◽  
Ring Form ◽  
Nilpotent Elements ◽  
Finite Dimensional ◽  
Rank One

Let [Formula: see text] be an arbitrary pointed Hopf algebra of rank one and [Formula: see text] the group of group-like elements of [Formula: see text]. In this paper, we give the decomposition of a tensor product of finite dimensional indecomposable right [Formula: see text]-comodules into a direct sum of indecomposables. This enables us to describe the corepresentation ring of [Formula: see text] in terms of generators and relations. Such a ring is not commutative if [Formula: see text] is not abelian. We describe all nilpotent elements of the corepresentation ring of [Formula: see text] if [Formula: see text] is a finite abelian group or a particular Hamiltonian group. In this case, all nilpotent elements of the corepresentation ring form a principal ideal which is either zero or generated by a nilpotent element of degree 2.

Continuous singular measures equivalent to their convolution squares

1976 ◽  
Vol 80 (2) ◽  
pp. 249-268 ◽  
Author(s):  
Gavin Brown ◽  
Edwin Hewitt
Keyword(s):  
Abelian Group ◽  
Haar Measure ◽  
Measure Algebra ◽  
Locally Compact ◽  
Character Group ◽  
Singular Measures ◽  
Continuous Measures ◽  
Discrete Abelian Group

Throughout this paper, G will denote a locally compact, non-discrete, Abelian group (subjected to various conditions) and X wi11 denote the character group of G. All terminology and notation are as in (7). The measure algebra M(G), as is known, is a very complicated entity. We address ourselves here to some novel peculiarities of the subspace Ms(G) of continuous measures in M(G) that are singular with respect to Haar measure λ.

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