14-Sets Algebra

Posted on Posted in Theory

A novel 14-D algebra based upon Kuratowski Monoid’s Closure and Complement operators is uncovered. 14×14 Matrix Representation, Conditions for inverse elements, 0-Commutator and Coproduct computed using Mathematica 9.0 . Almost Random Almost Incompressible large-length coefficients are found to have inverse. Matrix representation has the form of a Stochastic Matrix, and its infinite power has a limit with three 1-valued eigenvalues with determinant 0. As a consequence of this algebra, a topological (Twist on Z2xZ2xZ2) construction of the Octonions developed. An approximate Logarithmic algorithm devised for mapping Kuratowski’s topological operators to 182 dimensional Lie Algebra of 14×14 matrices with columns sum up to 0, thus a concept of pre-geometry is brought forth. De Novo semantics attributed to these 14-D vectors described, in categoreal form, borrowing from the seminal work of Alfred North Whitehead’s Process and Reality.

 

Algebra only all code removed:

http://files.lossofgenerality.com/14Sets_algebra.pdf

With code:

http://files.lossofgenerality.com/14sets_lowres.pdf 

http://files.lossofgenerality.com/14sets.pdf

http://files.lossofgenerality.com/14sets.nb