Spectra of locally matrix algebras

Oksana Bezushchak;

doi:10.12958/adm1734

Spectra of locally matrix algebras

Algebra and Discrete Mathematics ◽

10.12958/adm1734 ◽

2021 ◽

Vol 31 (1) ◽

pp. 17-36

Author(s):

Oksana Bezushchak ◽

Keyword(s):

Matrix Algebras

We describe spectra of associative (not necessarily unital and not necessarily countable-dimensional) locally matrix algebras. We determine all possible spectra of locally matrix algebras and give a new proof of Dixmier–Baranov Theorem. As an application of our description of spectra, we determine embeddings of locally matrix algebras.

Download Full-text

Notes on three-pass protocol

Herald of Omsk University ◽

10.24147/1812-3996.2020.25(4).4-9 ◽

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.

Download Full-text

τ-tilting finite triangular matrix algebras

Journal of Pure and Applied Algebra ◽

10.1016/j.jpaa.2021.106785 ◽

2021 ◽

pp. 106785

Author(s):

Takuma Aihara ◽

Takahiro Honma

Keyword(s):

Triangular Matrix ◽

Matrix Algebras

Download Full-text

Iterants, Majorana Fermions and the Majorana-Dirac Equation

Symmetry ◽

10.3390/sym13081373 ◽

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.

Download Full-text