Ultrametric continuous linear representations of the compact groups 𝑆𝐿(2,ℤ_{𝕡}) and 𝔾𝕃(2,ℤ_{𝕡})

2016 ◽  
pp. 41-56
Author(s):  
Bertin Diarra ◽  
Tongobè Mounkoro
Keyword(s):  
Compact Groups ◽  
Continuous Linear ◽  
Linear Representations

A complete reducible and an irreducible continuous linear representations

2015 ◽  
Vol 9 ◽  
pp. 2319-2326
Author(s):  
Diah Junia Eksi Palupi ◽  
Soeparna Darmawijaya ◽  
Setiadji ◽  
Ch. Rini Indrati
Keyword(s):  
Continuous Linear ◽  
Linear Representations

A Class of Abstract Linear Representations for Convolution Function Algebras over Homogeneous Spaces of Compact Groups

2018 ◽  
Vol 70 (1) ◽  
pp. 97-116 ◽  
Author(s):  
Arash Ghaani Farashahi
Keyword(s):  
Invariant Measure ◽  
Compact Group ◽  
Homogeneous Space ◽  
Closed Subgroup ◽  
Homogeneous Spaces ◽  
Compact Groups ◽  
Compact Homogeneous Space ◽  
Linear Representations ◽  
Function Algebras ◽  
Convolution Function

AbstractThis paper introduces a class of abstract linear representations on Banach convolution function algebras over homogeneous spaces of compact groups. LetGbe a compact group andHa closed subgroup ofG. Letμbe the normalizedG-invariant measure over the compact homogeneous spaceG/Hassociated with Weil's formula and. We then present a structured class of abstract linear representations of the Banach convolution function algebrasLp(G/H,μ).

scholarly journals ZERO JORDAN PRODUCT DETERMINED BANACH ALGEBRAS

2020 ◽  
pp. 1-14
Author(s):  
J. ALAMINOS ◽  
M. BREŠAR ◽  
J. EXTREMERA ◽  
A. R. VILLENA
Keyword(s):  
Banach Space ◽  
Banach Algebra ◽  
Banach Algebras ◽  
Group Algebras ◽  
Locally Compact Groups ◽  
Compact Groups ◽  
Continuous Linear ◽  
Bilinear Map ◽  
Locally Compact ◽  
Jordan Product

A Banach algebra $A$ is said to be a zero Jordan product determined Banach algebra if, for every Banach space $X$ , every bilinear map $\unicode[STIX]{x1D711}:A\times A\rightarrow X$ satisfying $\unicode[STIX]{x1D711}(a,b)=0$ whenever $a$ , $b\in A$ are such that $ab+ba=0$ , is of the form $\unicode[STIX]{x1D711}(a,b)=\unicode[STIX]{x1D70E}(ab+ba)$ for some continuous linear map $\unicode[STIX]{x1D70E}$ . We show that all $C^{\ast }$ -algebras and all group algebras $L^{1}(G)$ of amenable locally compact groups have this property and also discuss some applications.

On non-compact groups. II. Representations of the 2+1 Lorentz group

1965 ◽  
Vol 287 (1411) ◽  
pp. 532-548 ◽  
Keyword(s):  
Hilbert Space ◽  
Direct Product ◽  
Lorentz Group ◽  
Complex Number ◽  
Algebraic Method ◽  
Unitary Representations ◽  
Compact Groups ◽  
Matrix Elements ◽  
Linear Representations ◽  
The Matrix

A simple algebraic method based on multispinors with a complex number of indices is used to obtain the linear (and unitary) representations of non-com pact groups. The method is illustrated in the case of the 2+1 Lorentz group. All linear representations of this group, their various realizations in Hilbert space as well as the matrix elements of finite transformations have been found. The problem of reduction of the direct product is also briefly discussed.

On non-compact groups. III. The linear representations of widetilde{ SU } 3

1965 ◽  
Vol 288 (1412) ◽  
pp. 98-112 ◽  
Keyword(s):  
Elementary Particle ◽  
Compact Form ◽  
Isotopic Spin ◽  
Compact Groups ◽  
Infinite Dimensional ◽  
Linear Representations ◽  
Theoretical Predictions

We have studied the representations of a non-compact form widetilde{ SU } 3 of SU 3 , with emphasis on the unitary ones. Some of the representations, though infinite dimensional, appear to be eminently suitable for describing elementary particle multiplets. For baryons the only new particle of strangeness larger than—3 that is predicted is one with strangeness—2 and isotopic spin 3/2. The most important companion to the ‘decuplet ’ resonance is a Y* 2 . It seems likely that many theoretical predictions of SU 3 are carried over to widetilde{ SU } 3 .

Sign in / Sign up

Export Citation Format

Share Document