finsler geometry, hypercomplex numbers and physics
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NULLVECTOR ALGEBRA
2015jlv | S.Ya. Kotkovsky  // s_kotkovsky@mail.ru

In this paper, we study the properties of biquaternionic divisors of zero («nullquaternions»). Subalgebra of nullquaternions is closely related to its subclass – «nullvectors», which are complex-valued three-dimension vectors, having zero square. Theorem of nullvector factorization shows that regular nullquaternion can be represented as product of two nullvectors belonging to uniquely defined classes, thus defining the structure of nullquaternion. Theorem of nullvector allelity proves that product of two nullquaternions preserves one of the structure halves of each multiplier. Last circumstance signs for prominent similarity of nullvector algebra with genetics: product of nullvectors is similar to combination of genes in chromosome. We show, that along with nullvectors there exist «uniform» classes of nullquaternions which are isomorphic to nullvector classes. Regular, uniform nullquaternions and nullvectors represent general classification of nullquaternions with relation to multiplication.


English: Russian:
09_hngp23_kotkovsky.pdf, 154,869 Kb, PDF

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