Structure of Basic Lie Superalgebras and of Their Affine Extensions - INSPIRE

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Structure of Basic Lie Superalgebras and of Their Affine Extensions

L. Frappat
(
- Annecy, LAPP and
- Savoie U.
)
,
A. Sciarrino
(
- Naples U. and
- INFN, Naples
)
,
P. Sorba
(
- Annecy, LAPP
)

Dec, 1987

40 pages

Published in:

Commun.Math.Phys. 121 (1989) 457-500

DOI:

10.1007/BF01217734

Report number:

LAPP-TH-207-87

reference search83 citations

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Abstract: (Springer)

We generalize to the case of superalgebras several properties of simple Lie algebras involving the use of Dynkin diagrams. If to a simple Lie algebra can be associated one Dynkin diagram, it is a finite set of nonequivalent ones which can be constructed for a basic superalgebra (or B.S.A.). The knowledge of these diagrams, which can be obtained for each B.S.A. in a systematic way, allows us to deduce the regular subsuperalgebras of a B.S.A. The symmetries of the Dynkin diagrams are related to outer automorphisms of B.S.A. and lead to some singular subsuperalgebras. Finally we consider the extended Dynkin diagrams in order to classify the affine B.S.A. and use their symmetries to construct the twisted basic superalgebras.

ALGEBRA: LIE
SUPERSYMMETRY
ALGEBRA: REPRESENTATION

References(15)

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