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Abstract
A symmetric supermanifold is defined as a supermanifold $\chi$ endowed with a morphism $\mu$: $\chi\times\chi\to\chi$ satisfying three algebraic properties and a local condition.
To each symmetric supermanifold $\chi$ we associate a Lie triple supersystem, denoted by ${\cal D}$ -($\chi$), and obtain a one-to-one correspondence between simply connected symmetric supermanifolds and Lie triple supersystems. We then show that a symmetric supermanifold is homogeneous. After defining Jordan triples, we show the existence of a distinguished boundary for the symmetric superdomains Gr$\sp\*$ and QGr$\sp\*$.
Details
Title
Symmetric supermanifolds and Lie triple supersystems
Author
Vinel, Gerard Francois
Year
1990
ISBN
979-8-207-78207-2
Source type
Dissertation or Thesis
Language of publication
English
ProQuest document ID
303821725
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
