Algebra

1911 Submissions

[5] viXra:1911.0275 [pdf] replaced on 2019-11-17 23:52:46

Exponential Factorization and Polar Decomposition of Multivectors in $Cl(p,q)$, $p+q \leq 3$

Authors: Eckhard Hitzer, Stephen J. Sangwine
Comments: 18 Pages. Submitted to Adv. in Appl. Cliff. Algs., 2019.

In this paper we consider general multivector elements of Clifford algebras $Cl(p,q)$, $n=p+q \leq 3$, and study multivector equivalents of polar decompositions and factorization into products of exponentials, where the exponents are frequently blades of grades zero (scalar) to $n$ (pseudoscalar).
Category: Algebra

[4] viXra:1911.0258 [pdf] submitted on 2019-11-15 06:50:19

Refutation of Fundamental Sets for Algebraic Subgroups

Authors: Colin James III
Comments: 2 Pages. © Copyright 2019 by Colin James III All rights reserved. Note that Disqus comments here are not read by the author; reply by email only to: info@cec-services dot com. Include a list publications for veracity. Updated abstract at ersatz-systems.com.

We evaluate fundamental sets for algebraic subgroups by way of the seminal Theorem 6.12. It is not tautologous and refutes the conjecture. What follows is refutation of quantitative reduction theory and unlikely intersections. These results form a non tautologous fragment of the universal logic VŁ4.
Category: Algebra

[3] viXra:1911.0226 [pdf] submitted on 2019-11-12 10:50:35

Hypercomplex Numbers of Dimension 11

Authors: Valery Timin
Comments: timinva@yandex.ru, 3 pages in Russian

This work is devoted to the search, study and compilation of the multiplication table of a compound hyperbolic (Hypercomplex) number of dimension nine (11): q = {1, i1, i2, i3, …, i10, }: in2 = 1. On this basis, as a template, you can choose other multiplication tables with a different target or arbitrary arrangement of plus (+) and minus (-) characters in the cells of the multiplication table. The disadvantage of multiplication tables of dimension 11 is that they are neither associative nor commutative (not even anticommutative). But this is their fundamental property.. Эта работа посвящена поиску, изучению и составлению таблицы умножения составного гиперболического (гиперкомплексного) числа размерностью девять (11): q = {1, i1, i2, i3, …, i11, }: in2 = 1. На этой основе как на шаблоне можно подобрать другие таблицы умножения с другой целевой или произвольной расстановкой знаков "плюс" (+) и "минус" (-) в ячейках таблицы умножения. Ассоциативных и коммутативных таблиц умножения не имеется.
Category: Algebra

[2] viXra:1911.0174 [pdf] submitted on 2019-11-09 04:11:04

On the Construction of a Regular Heptagon by Straightedge and Compass

Authors: Henry Wong
Comments: 1 Page.

An addendum to field theory.
Category: Algebra

[1] viXra:1911.0023 [pdf] submitted on 2019-11-01 12:27:07

Cheating with Complex Numbers Der Selbstbetrug Mit Den Komplexen Zahlen

Authors: Martin Erik Horn
Comments: 6 pages, bilingual version (in English and German)

Together with complex conjugation, complex numbers are misused to model anti-commutative structures. German Abstract: Komplexe Zahlen werden zur Modellierung anti-kommutativer Strukturen missbraucht, wenn die komplexe Konjugation genutzt wird.
Category: Algebra