Algebra

1901 Submissions

[3] viXra:1901.0246 [pdf] submitted on 2019-01-16 21:58:12

Construction of Multivector Inverse for Clif Ford Algebras Over 2m+1-Dimensional Vector Spaces from Multivector Inverse for Clifford Algebras Over 2m-Dimensional Vector Spaces

Authors: Eckhard Hitzer, Stephen J. Sangwine
Comments: 23 Pages. Accepted by Adv. in Applied Cliff. Algebras, 2019.

Assuming known algebraic expressions for multivector inverses in any Clifford algebra over an even dimensional vector space R^{p',q'), n' = p' +q' = 2m, we derive a closed algebraic expression for the multivector inverse over vector spaces one dimension higher, namely over R^{p,q}, n = p+q = p'+q'+1 = 2m+1. Explicit examples are provided for dimensions n' = 2,4,6, and the resulting inverses for n = n' +1 = 3,5,7. The general result for n = 7 appears to be the first ever reported closed algebraic expression for a multivector inverse in Clifford algebras Cl(p,q), n = p + q = 7, only involving a single addition of multivector products in forming the determinant.
Category: Algebra

[2] viXra:1901.0142 [pdf] submitted on 2019-01-10 08:52:27

Classification Des Formes Quadratiques

Authors: BOUCHOUAT El Mehdi
Comments: 23 Pages.

La théorie des formes quadratiques est très vaste et dans ce mémoire je n'en mentionne qu'une très petite partie. Dans la première section, j'introduis les formes quadratiques et leurs formes bilinéaires associées et je présente quelques résultats généraux. La deuxième section est consacrée à la classification des formes quadratiques sur $\mathbb{C}$, $\mathbb{R}$, et sur les corps finis $\mathbb{F}_{q}$, et dans la troisième section je me concentre sur l'une des applications de la classification des formes quadratiques : La loi de réciprocité quadratique.
Category: Algebra

[1] viXra:1901.0128 [pdf] submitted on 2019-01-09 09:14:26

The Modified Clifford Algebra

Authors: Antoine Balan
Comments: 1 page, written in english

We propose here a modification of the Clifford algebra with relations using three vectors instead of two.
Category: Algebra