Abstract/Details

Symmetric supermanifolds and Lie triple supersystems

Vinel, Gerard Francois. 
 University of Connecticut ProQuest Dissertations Publishing,  1990. 9106365.

Abstract (summary)

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$\sp\*$.

Indexing (details)


Subject
Mathematics
Classification
0405: Mathematics
Identifier / keyword
Pure sciences; Jordan triples; supermanifolds
Title
Symmetric supermanifolds and Lie triple supersystems
Author
Vinel, Gerard Francois
Number of pages
97
Degree date
1990
School code
0056
Source
DAI-B 51/09, Dissertation Abstracts International
Place of publication
Ann Arbor
Country of publication
United States
ISBN
979-8-207-78207-2
Advisor
Abikoff, William
University/institution
University of Connecticut
University location
United States -- Connecticut
Degree
Ph.D.
Source type
Dissertation or Thesis
Language
English
Document type
Dissertation/Thesis
Dissertation/thesis number
9106365
ProQuest document ID
303821725
Copyright
Database copyright ProQuest LLC; ProQuest does not claim copyright in the individual underlying works.
Document URL
https://www.proquest.com/docview/303821725/abstract