Authors: Martin Erik Horn
Comments: 25 Pages. 6 Figures.
Quarks are described mathematically by (3 x 3) matrices. To include these quarkonian mathematical structures into Geometric Algebra it is helpful to restate Geometric Algebra in the
mathematical language of (3 x 3) matrices. It will be shown in this paper how (3 x 3) permutation matrices can be interpreted as unit vectors. Special emphasis will be given to the definition of some wedge products which fifit better to this algebra of (3 x 3) matrices than the usual Geometric Algebra wedge product. And as S3 permutation symmetry is flavour symmetry a unifified flavour picture of Geometric Algebra will emerge.
In this book, the authors introduce the notion of quasi set topological vector subspaces. The
advantage of such study is that given a vector subspace we can have only one topological
space associated with the collection of all subspaces. However, we can have several
quasi set topological vector subspaces of a given vector space. Further, we have defined
topological spaces for set vector spaces, semigroup vector spaces and group vector spaces.