English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The questions on the existence of the three color quark symmetry and three quark-lepton generations could have the origin associated with the new exotic symmetries outside the Cartan-Killing-Lie algebras/groups. Our long-term search for these symmetries has been began with our Calabi-Yau space classification on the basis of the n-ary algebra for the reflexive projective numbers and led us to the expansion of the binary  n  = 2 complex and hyper complex numbers in the framework of the n-ary complex and hyper-complex numbers with  n  = 3, 4, … where we constructed new Abelian and non-Abelian symmetries. We have studied then norm-division properties of the Abelian nary complex numbers and have built the infinite chain of the Abelian groups  U  ( n –1)  = [ U (1) × … ×  U (1)] ( n –1) . We have developed the n-ary holomorphic (polymorphic) analysis on the n-ary complex space  NC  { n } , which led us to the generalization of the quadratic Laplace equations for the harmonic functions. The generalized Laplace equations for the n-ary harmonic functions give us the n-th order homogeneous differential equations which are invariant with respect to the Abelian n-ary groups  U  ( n –1)  and with some new spatial properties. Further consideration of the non-Abelian n-ary hyper-complex numbers opens the infinite series of the non-Abelian  T n SU ( n )-Lie groups(n=3,4,…) and its corresponding  t n su ( n ) algebras. One of the exceptional features of these symmetry groups is the appearance of some new n-dimensional spinors that could lead to an extension of the concept of the  SU (2)-spin, to the appearance of n-dimensional quantum structures -exotic “n-spinor” matter( n  = 3, 4, … - maarcrions). It is natural to assume that these new exotic “quantum spinor states” could be candidates for the pra-matter of the quark-charge leptons or/and for the dark matter. We will be also interested in the detection of the exotic quantum ’n-spinor” matter in the neutrino and hadron experiments.

Ternary SU(3)-group symmetry and its possible applications in hadron-quark substructure. Towards a new spinor-fermion structure