We discuss (Formula presented.) Klein and Klein-conformal superspaces in (Formula presented.) space-time dimensions, realizing them in terms of their functor of points over the split composition algebra (Formula presented.). We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras. This leads to a natural interpretation of the sections of the spinor bundle in the critical split dimensions (Formula presented.) and (Formula presented.) as (Formula presented.), (Formula presented.) and (Formula presented.), respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-conformal superspace structure.

Klein and conformal superspaces, split algebras and spinor orbits

FIORESI, RITA;LATINI, EMANUELE;
2017

Abstract

We discuss (Formula presented.) Klein and Klein-conformal superspaces in (Formula presented.) space-time dimensions, realizing them in terms of their functor of points over the split composition algebra (Formula presented.). We exploit the observation that certain split forms of orthogonal groups can be realized in terms of matrix groups over split composition algebras. This leads to a natural interpretation of the sections of the spinor bundle in the critical split dimensions (Formula presented.) and (Formula presented.) as (Formula presented.), (Formula presented.) and (Formula presented.), respectively. Within this approach, we also analyze the non-trivial spinor orbit stratification that is relevant in our construction since it affects the Klein-conformal superspace structure.
Fioresi, Rita; Latini, Emanuele; Marrani, Alessio
File in questo prodotto:
Eventuali allegati, non sono esposti

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/625456
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 3
  • ???jsp.display-item.citation.isi??? 4
social impact