scholarly journals Wreath products with the integers, proper actions and Hilbert space compression

2007 ◽  
Vol 124 (1) ◽  
pp. 199-211 ◽  
Author(s):  
Yves Stalder ◽  
Alain Valette
Keyword(s):  
Hilbert Space ◽  
Wreath Products ◽  
Proper Actions ◽  
Space Compression

scholarly journals Proper actions of wreath products and generalizations

2012 ◽  
Vol 364 (6) ◽  
pp. 3159-3184 ◽  
Author(s):  
Yves Cornulier ◽  
Yves Stalder ◽  
Alain Valette
Keyword(s):  
Wreath Products ◽  
Proper Actions

scholarly journals Multipartite Quantum Systems and Representations of Wreath Products

2020 ◽  
Vol 226 ◽  
pp. 02013
Author(s):  
Vladimir Kornyak
Keyword(s):  
Hilbert Space ◽  
Quantum Correlations ◽  
Wreath Products ◽  
Quantum Systems ◽  
Efficient Computation ◽  
Multipartite Quantum Systems ◽  
Irreducible Components ◽  
Local Correlations ◽  
Non Local ◽  
Multipartite System

The multipartite quantum systems are of particular interest for the study of such phenomena as entanglement and non-local correlations. The symmetry group of the whole multipartite system is the wreath product of the group acting in the “local” Hilbert space and the group of permutations of the constituents. The dimension of the Hilbert space of a multipartite system depends exponentially on the number of constituents, which leads to computational difficulties. We describe an algorithm for decomposing representations of wreath products into irreducible components. The C implementation of the algorithm copes with representations of dimensions in quadrillions. The program, in particular, builds irreducible invariant projectors in the Hilbert space of a multipartite system. The expressions for these projectors are tensor product polynomials. This structure is convenient for efficient computation of quantum correlations in multipartite systems with a large number of constituents.

scholarly journals Hilbert space compression and exactness of discrete groups

2005 ◽  
Vol 222 (2) ◽  
pp. 292-305 ◽  
Author(s):  
Sarah Campbell ◽  
Graham A. Niblo
Keyword(s):  
Hilbert Space ◽  
Discrete Groups ◽  
Space Compression

EMBEDDABILITY OF GENERALISED WREATH PRODUCTS

2014 ◽  
Vol 91 (2) ◽  
pp. 250-263 ◽  
Author(s):  
CHRIS CAVE ◽  
DENNIS DREESEN
Keyword(s):  
Hilbert Space ◽  
Wreath Product ◽  
Metric Spaces ◽  
Wreath Products ◽  
Finitely Generated ◽  
Product Construction ◽  
Finitely Generated Groups

AbstractGiven two finitely generated groups that coarsely embed into a Hilbert space, it is known that their wreath product also embeds coarsely into a Hilbert space. We introduce a wreath product construction for general metric spaces $X,Y,Z$ and derive a condition, called the (${\it\delta}$-polynomial) path lifting property, such that coarse embeddability of $X,Y$ and $Z$ implies coarse embeddability of $X\wr _{Z}Y$. We also give bounds on the compression of $X\wr _{Z}Y$ in terms of ${\it\delta}$ and the compressions of $X,Y$ and $Z$.

Representation Theory and Harmonic Analysis of Wreath Products of Finite Groups

2009 ◽  
Author(s):  
Tullio Ceccherini-Silberstein ◽  
Fabio Scarabotti ◽  
Filippo Tolli
Keyword(s):  
Representation Theory ◽  
Harmonic Analysis ◽  
Finite Groups ◽  
Wreath Products

Hilbert Space

1993 ◽  
Author(s):  
J. R. Retherford
Keyword(s):  
Hilbert Space
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