The length function and matrix algebras

This chapter considers the notion of parallel residues in a building. It begins with the assumption that Δ‎ is a building of type Π‎, which is arbitrary except in a few places where it is explicitly assumed to be spherical. Δ‎ is not assumed to be thick. The chapter then elaborates on a hypothesis which states that S is the vertex set of Π‎, (W, S) is the corresponding Coxeter system, d is the W-distance function on the set of ordered pairs of chambers of Δ‎, and ℓ is the length function on (W, S). It also presents a notation in which the type of a residue R is denoted by Typ(R) and concludes with the condition that residues R and T of a building will be called parallel if R = projR(T) and T = projT(R).

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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.

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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

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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.

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