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 Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A semi-simple tensor extension of the Poincar\'e algebra is given for thearbitrary dimensions $D$. It is illustrated that this extension is a direct sumof the $D$-dimensional Lorentz algebra $so(D-1,1)$ and $D$-dimensional anti-deSitter (AdS) algebra $so(D-1,2)$. A supersymmetric also semi-simple $o(N)$generalization of this extension is introduced in the D=4 dimensions. It isestablished that this generalization is a direct sum of the 4-dimensionalLorentz algebra $so(3,1)$ and orthosymplectic algebra $osp(N,4)$ (super-AdSalgebra). Quadratic Casimir operators for the generalization are constructed.The form of these operators indicates that the components of an irreduciblerepresentation for this generalization are distinguished by the mass, angularmomentum and quantum numbers corresponding to the internal symmetry, tensor andsupersymmetry generators. That generalizes the Regge trajectory idea.  The probable unification of the N=10 supergravity with the SO(10) GUT modelis discussed.  This paper is dedicated to the memory of Anna Yakovlevna Gelyukh.

Semi-simple $o(N)$-extended super-Poincar\'e algebra