scholarly journals A CONSTRUCTION OF MAXIMAL COMMUTATIVE SUBALGEBRA OF MATRIX ALGEBRAS

2003 ◽  
Vol 40 (2) ◽  
pp. 241-250 ◽  
Author(s):  
Young-Kwon Song
Keyword(s):  
Matrix Algebras ◽  
Commutative Subalgebra ◽  
Maximal Commutative Subalgebra

scholarly journals Cocommutative elements form a maximal commutative subalgebra in quantum matrices

2018 ◽  
Vol 17 (09) ◽  
pp. 1850179
Author(s):  
Szabolcs Mészáros
Keyword(s):  
Trace Formula ◽  
Quantum Matrices ◽  
Root Of Unity ◽  
Commutative Subalgebra ◽  
Maximal Commutative Subalgebra ◽  
Coordinate Rings

In this paper, we prove that the subalgebras of cocommutative elements in the quantized coordinate rings of [Formula: see text], [Formula: see text] and [Formula: see text] are the centralizers of the trace [Formula: see text] in each algebra, for [Formula: see text] being not a root of unity. In particular, it is not only a commutative subalgebra as it was known before, but it is a maximal one.

scholarly journals MAXIMAL COMMUTATIVE SUBALGEBRAS INVARIANT FOR CP-MAPS: (COUNTER-)EXAMPLES

2008 ◽  
Vol 11 (04) ◽  
pp. 523-539 ◽  
Author(s):  
B. V. RAJARAMA BHAT ◽  
FRANCO FAGNOLA ◽  
MICHAEL SKEIDE
Keyword(s):  
Von Neumann Algebra ◽  
Von Neumann ◽  
Commutative Subalgebra ◽  
Commutative Subalgebras ◽  
Maximal Commutative Subalgebra

We solve, mainly by counterexamples, many natural questions regarding maximal commutative subalgebras invariant under CP-maps or semigroups of CP-maps on a von Neumann algebra. In particular, we discuss the structure of the generators of norm continuous semigroups on [Formula: see text] leaving a maximal commutative subalgebra invariant and show that there exist Markov CP-semigroups on Md without invariant maximal commutative subalgebras for any d > 2.

A Maximality Criterion for Nilpotent Commutative Matrix Algebras

1974 ◽  
Vol 17 (1) ◽  
pp. 125-126
Author(s):  
D. Handelman ◽  
P. Selick
Keyword(s):  
Commutative Algebra ◽  
Nilpotency Class ◽  
Matrix Algebras ◽  
Commutative Subalgebra ◽  
Commutative Matrix

Let A be a commutative algebra contained in Mn(F), F a field. Then A is nilpotent if there exists v such that Av=(0), and is said to have nilpotency class k (denoted Cl(A)=k) if Ak=(0), but Ak-1≠(0). A well known result asserts that matrix algebras are nilpotent if and only if every element is nilpotent. Let N = {A | A is a nilpotent commutative subalgebra of Mn(F)}.

scholarly journals Maximal commutative subalgebras of a Grassmann algebra

2019 ◽  
Vol 18 (07) ◽  
pp. 1950139
Author(s):  
Victor A. Bovdi ◽  
Ho-Hon Leung
Keyword(s):  
Grassmann Algebra ◽  
New Approach ◽  
Commutative Subalgebra ◽  
Intersecting Family ◽  
Grassmann Algebras ◽  
Commutative Subalgebras ◽  
Maximal Commutative Subalgebra

We provide a new approach to the investigation of maximal commutative subalgebras (with respect to inclusion) of Grassmann algebras. We show that finding a maximal commutative subalgebra in Grassmann algebras is equivalent to constructing an intersecting family of subsets of various odd sizes in [Formula: see text] which satisfies certain combinatorial conditions. Then we find new maximal commutative subalgebras in the Grassmann algebra of odd rank [Formula: see text] by constructing such combinatorial systems for odd [Formula: see text]. These constructions provide counterexamples to conjectures made by Domoskos and Zubor.

Notes on three-pass protocol

2020 ◽  
Vol 25 (4) ◽  
pp. 4-9
Author(s):  
Yerzhan R. Baissalov ◽  
Ulan Dauyl
Keyword(s):  
Finite Fields ◽  
Matrix Algebras ◽  
Associative Structures

The article discusses primitive, linear three-pass protocols, as well as three-pass protocols on associative structures. The linear three-pass protocols over finite fields and the three-pass protocols based on matrix algebras are shown to be cryptographically weak.

scholarly journals Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1373
Author(s):  
Louis H. Kauffman
Keyword(s):  
Dirac Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Clifford Algebras ◽  
Discrete Systems ◽  
Complex Numbers ◽  
Majorana Fermions ◽  
Matrix Algebras ◽  
Dirac Equations ◽  
Points Of View

This paper explains a method of constructing algebras, starting with the properties of discrimination in elementary discrete systems. We show how to use points of view about these systems to construct what we call iterant algebras and how these algebras naturally give rise to the complex numbers, Clifford algebras and matrix algebras. The paper discusses the structure of the Schrödinger equation, the Dirac equation and the Majorana Dirac equations, finding solutions via the nilpotent method initiated by Peter Rowlands.

On a Class of Automaton Algebras

2016 ◽  
Vol 60 (1) ◽  
pp. 31-38 ◽  
Author(s):  
Ferran Cedó ◽  
Jan Okniński
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Module ◽  
Commutative Subalgebra

AbstractWe show that every finitely generated algebra that is a finitely generated module over a finitely generated commutative subalgebra is an automaton algebra in the sense of Ufnarovskii.

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