scholarly journals On Fourier algebra homomorphisms

2004 ◽  
Vol 213 (1) ◽  
pp. 88-110 ◽  
Author(s):  
Monica Ilie
Keyword(s):  
Fourier Algebra ◽  
Algebra Homomorphisms

scholarly journals Completely bounded bimodule maps and spectral synthesis

2017 ◽  
Vol 28 (10) ◽  
pp. 1750067 ◽  
Author(s):  
M. Alaghmandan ◽  
I. G. Todorov ◽  
L. Turowska
Keyword(s):  
Tensor Product ◽  
Compact Group ◽  
Closed Subset ◽  
Spectral Synthesis ◽  
Locally Compact Group ◽  
Product Formula ◽  
Fourier Algebra ◽  
Locally Compact ◽  
Multiplication Algebra

We initiate the study of the completely bounded multipliers of the Haagerup tensor product [Formula: see text] of two copies of the Fourier algebra [Formula: see text] of a locally compact group [Formula: see text]. If [Formula: see text] is a closed subset of [Formula: see text] we let [Formula: see text] and show that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] then [Formula: see text] is a set of local spectral synthesis for [Formula: see text]. Conversely, we prove that if [Formula: see text] is a set of spectral synthesis for [Formula: see text] and [Formula: see text] is a Moore group then [Formula: see text] is a set of spectral synthesis for [Formula: see text]. Using the natural identification of the space of all completely bounded weak* continuous [Formula: see text]-bimodule maps with the dual of [Formula: see text], we show that, in the case [Formula: see text] is weakly amenable, such a map leaves the multiplication algebra of [Formula: see text] invariant if and only if its support is contained in the antidiagonal of [Formula: see text].

Gocommutative Hopf Algebras

1967 ◽  
Vol 19 ◽  
pp. 350-360 ◽  
Author(s):  
Richard G. Larson
Keyword(s):  
Hopf Algebra ◽  
Vector Space ◽  
Hopf Algebras ◽  
Image Position ◽  
Algebra Homomorphisms

A coalgebra over the field F is a vector space A over F, with maps δ: A → A ⊗ A and ∊: A → F such that1and2The notion of coalgebra is dual to the notion of algebra with unit, with δ as coproduct (equation (1) says that δ is associative) and ∊ as the unit map (equation (2) is just the statement that ∊ is a unit for the coproduct δ). If A is also an algebra with unit and δ and ∊ are algebra homomorphisms, A is a Hopf algebra.

scholarly journals Amenability properties of the central Fourier algebra of a compact group

2016 ◽  
Vol 60 (2) ◽  
pp. 505-527
Author(s):  
Mahmood Alaghmandan ◽  
Nico Spronk
Keyword(s):  
Compact Group ◽  
Fourier Algebra

scholarly journals Lifts of Symmetric Tensors: Fluids, Plasma, and Grad Hierarchy

Entropy ◽  
2019 ◽  
Vol 21 (9) ◽  
pp. 907 ◽  
Author(s):  
Oğul Esen ◽  
Miroslav Grmela ◽  
Hasan Gümral ◽  
Michal Pavelka
Keyword(s):  
Kinetic Theory ◽  
Lie Algebra ◽  
Particle Motion ◽  
Evolution Equations ◽  
Poisson Brackets ◽  
Hamiltonian Approach ◽  
Symmetric Tensors ◽  
Field Equations ◽  
Algebra Homomorphisms

Geometrical and algebraic aspects of the Hamiltonian realizations of the Euler’s fluid and the Vlasov’s plasma are investigated. A purely geometric pathway (involving complete lifts and vertical representatives) is proposed, which establishes a link from particle motion to evolution of the field variables. This pathway is free from Poisson brackets and Hamiltonian functionals. Momentum realizations (sections on T * T * Q ) of (both compressible and incompressible) Euler’s fluid and Vlasov’s plasma are derived. Poisson mappings relating the momentum realizations with the usual field equations are constructed as duals of injective Lie algebra homomorphisms. The geometric pathway is then used to construct the evolution equations for 10-moments kinetic theory. This way the entire Grad hierarchy (including entropic fields) can be constructed in a purely geometric way. This geometric way is an alternative to the usual Hamiltonian approach to mechanics based on Poisson brackets.

scholarly journals Weak homomorphisms between functorial algebras

2011 ◽  
Vol 44 (4) ◽  
Author(s):  
Friedrich Martin Schneider
Keyword(s):  
Universal Algebra ◽  
Similarity Type ◽  
Algebra Homomorphisms

AbstractIn universal algebra, homomorphisms are usually considered between algebras of the same similarity type. Different from that, the notion of a weak homomorphism, as introduced by E. Marczewski in 1961, does not depend on a signature, but only on the clones of term operations generated by the examined algebras. We generalize this idea by defining weak homomorphisms between

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