GRADED IDENTITIES FOR THE MATRIX ALGEBRA OF ORDER OVER AN INFINITE FIELD

2002 ◽  
Vol 30 (12) ◽  
pp. 5849-5860 ◽  
Author(s):  
Sergio S. Azevedo
Keyword(s):  
Matrix Algebra ◽  
Infinite Field ◽  
Graded Identities ◽  
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.

A note on graded polynomial identities for tensor products by the Grassmann algebra in positive characteristic

2016 ◽  
Vol 26 (06) ◽  
pp. 1125-1140 ◽  
Author(s):  
Lucio Centrone ◽  
Viviane Ribeiro Tomaz da Silva
Keyword(s):  
Positive Characteristic ◽  
Finite Abelian Group ◽  
Grassmann Algebra ◽  
Graded Algebra ◽  
Infinite Field ◽  
Infinite Dimensional ◽  
Graded Identities ◽  
Graded Polynomial Identities ◽  
Specific Formula ◽  
Gk Dimension

Let [Formula: see text] be a finite abelian group. As a consequence of the results of Di Vincenzo and Nardozza, we have that the generators of the [Formula: see text]-ideal of [Formula: see text]-graded identities of a [Formula: see text]-graded algebra in characteristic 0 and the generators of the [Formula: see text]-ideal of [Formula: see text]-graded identities of its tensor product by the infinite-dimensional Grassmann algebra [Formula: see text] endowed with the canonical grading have pairly the same degree. In this paper, we deal with [Formula: see text]-graded identities of [Formula: see text] over an infinite field of characteristic [Formula: see text], where [Formula: see text] is [Formula: see text] endowed with a specific [Formula: see text]-grading. We find identities of degree [Formula: see text] and [Formula: see text] while the maximal degree of a generator of the [Formula: see text]-graded identities of [Formula: see text] is [Formula: see text] if [Formula: see text]. Moreover, we find a basis of the [Formula: see text]-graded identities of [Formula: see text] and also a basis of multihomogeneous polynomials for the relatively free algebra. Finally, we compute the [Formula: see text]-graded Gelfand–Kirillov (GK) dimension of [Formula: see text].

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]

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