scholarly journals Recurrence, rigidity, and popular differences

2017 ◽  
Vol 39 (5) ◽  
pp. 1299-1316 ◽  
Author(s):  
JOHN T. GRIESMER
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Weak Mixing ◽  
Bohr Topology

We construct a set of integers $S$ such that every translate of $S$ is a set of recurrence and a set of rigidity for a weak mixing measure preserving system. Here ‘set of rigidity’ means that enumerating $S$ as $(s_{n})_{n\in \mathbb{N}}$ produces a rigidity sequence. This construction generalizes or strengthens results of Katznelson, Saeki (on equidistribution and the Bohr topology), Forrest (on sets of recurrence and strong recurrence), and Fayad and Kanigowski (on rigidity sequences). The construction also provides a density analogue of Julia Wolf’s results on popular differences in finite abelian groups.

scholarly journals EXAMPLES OF FINITE-DIMENSIONAL POINTED HOPF ALGEBRAS IN CHARACTERISTIC 2

2020 ◽  
pp. 1-14
Author(s):  
NICOLÁS ANDRUSKIEWITSCH ◽  
DIRCEU BAGIO ◽  
SARADIA DELLA FLORA ◽  
DAIANA FLÔRES
Keyword(s):  
Hopf Algebras ◽  
Abelian Groups ◽  
Vector Spaces ◽  
Group Algebras ◽  
Finite Abelian Groups ◽  
Finite Dimensional ◽  
Pointed Hopf Algebras ◽  
Characteristic 2 ◽  
Nichols Algebras ◽  
Kirillov Dimension

Abstract We present new examples of finite-dimensional Nichols algebras over fields of characteristic 2 from braided vector spaces that are not of diagonal type, admit realizations as Yetter–Drinfeld modules over finite abelian groups, and are analogous to Nichols algebras of finite Gelfand–Kirillov dimension in characteristic 0. New finite-dimensional pointed Hopf algebras over fields of characteristic 2 are obtained by bosonization with group algebras of suitable finite abelian groups.

scholarly journals Sum-free subsets of finite abelian groups of type III

2016 ◽  
Vol 58 ◽  
pp. 181-202 ◽  
Author(s):  
R. Balasubramanian ◽  
Gyan Prakash ◽  
D.S. Ramana
Keyword(s):  
Abelian Groups ◽  
Finite Abelian Groups ◽  
Type Iii
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