scholarly journals Unital decompositions of the matrix algebra of order three

2021 ◽  
pp. 1-26
Author(s):  
V. Gubarev
Keyword(s):  
Matrix Algebra ◽  
The Matrix

A New Spectral Approach in the Matrix Algebra: C-Determinant Pseudospectrum

2021 ◽  
Vol 65 (7) ◽  
pp. 1-7
Author(s):  
Aymen Ammar ◽  
Aref Jeribi ◽  
Kamel Mahfoudhi
Keyword(s):  
Matrix Algebra ◽  
Spectral Approach ◽  
The Matrix

Johnson pseudo-contractibility of second duals of certain Banach algebras

2019 ◽  
pp. 2150012
Author(s):  
A. Sahami ◽  
E. Ghaderi ◽  
S. M. Kazemi Torbaghan ◽  
B. Olfatian Gillan
Keyword(s):  
Tensor Product ◽  
Matrix Algebra ◽  
Banach Algebras ◽  
Amenable Group ◽  
Semigroup Algebra ◽  
Archimedean Semigroup ◽  
Projective Tensor Product ◽  
Projective Tensor ◽  
The Matrix ◽  
Second Dual

In this paper, we study Johnson pseudo-contractibility of second dual of some Banach algebras. We show that the semigroup algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is a finite amenable group, where [Formula: see text] is an archimedean semigroup. We also show that the matrix algebra [Formula: see text] is Johnson pseudo-contractible if and only if [Formula: see text] is finite. We study Johnson pseudo-contractibility of certain projective tensor product second duals Banach algebras.

scholarly journals FUZZY INSTANTONS

2002 ◽  
Vol 17 (15) ◽  
pp. 2095-2111 ◽  
Author(s):  
HARALD GROSSE ◽  
MARCO MACEDA ◽  
JOHN MADORE ◽  
HAROLD STEINACKER
Keyword(s):  
Real Number ◽  
Matrix Model ◽  
Matrix Algebra ◽  
Quantization Condition ◽  
Constant Factor ◽  
Arbitrary Real Number ◽  
Self Duality ◽  
Duality Condition ◽  
The Matrix ◽  
Fixed Constant

We present a series of instanton-like solutions to a matrix model which satisfy a self-duality condition and possess an action whose value is, to within a fixed constant factor, an integer l2. For small values of the dimension n2 of the matrix algebra the integer resembles the result of a quantization condition but as n → ∞ the ratio l/n can tend to an arbitrary real number between zero and one.

Factorization of the algebra of particles of half-odd spin

1952 ◽  
Vol 48 (1) ◽  
pp. 110-117
Author(s):  
K. J. Le Couteur
Keyword(s):  
Wave Equation ◽  
Direct Product ◽  
Matrix Algebra ◽  
Relativistic Wave Equation ◽  
Relativistic Wave ◽  
Original Matrix ◽  
Dirac Algebra ◽  
The Matrix ◽  
Integral Spin

AbstractIt is proved that the matrix algebra for any relativistic wave equation of half-odd integral spin can be factorized as the direct product of a Dirac algebra and another, called a ξ-algebra. The structure and representation of ξ-algebras are studied in detail. The factorization simplifies calculations with particles of spin > ½, because the ξ-algebra contains only one-sixteenth as many elements as the original matrix algebra.

On associative representations of non-associative algebras

2018 ◽  
Vol 17 (03) ◽  
pp. 1850051 ◽  
Author(s):  
A. I. Kornev ◽  
I. P. Shestakov
Keyword(s):  
Matrix Algebra ◽  
Poisson Algebra ◽  
Associative Algebras ◽  
The Matrix ◽  
Dickson Algebra

We define a notion of associative representation for algebras. We prove the existence of faithful associative representations for any alternative, Mal’cev, and Poisson algebra, and prove analogs of Ado-Iwasawa theorem for each of these cases. We construct also an explicit associative representation of the Cayley–Dickson algebra in the matrix algebra [Formula: see text]

scholarly journals A FINITE QUANTUM SYMMETRY OF $M(3, {\Bbb C})$

1998 ◽  
Vol 13 (24) ◽  
pp. 4147-4161 ◽  
Author(s):  
LUDWIK DABROWSKI ◽  
FABRIZIO NESTI ◽  
PASQUALE SINISCALCO
Keyword(s):  
Standard Model ◽  
Exact Sequence ◽  
Hopf Algebra ◽  
Quantum Group ◽  
Recent Work ◽  
Quantum Groups ◽  
Matrix Algebra ◽  
Group Symmetry ◽  
The Standard Model ◽  
The Matrix

The 27-dimensional Hopf algebra A(F), defined by the exact sequence of quantum groups [Formula: see text], [Formula: see text], is studied as a finite quantum group symmetry of the matrix algebra [Formula: see text], describing the color sector of Alain Connes' formulation of the Standard Model. The duality with the Hopf algebra ℋ, investigated in a recent work by Robert Coquereaux, is established and used to define a representation of ℋ on [Formula: see text] and two commuting representation of ℋ on A(F).

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