We present a construction “a` la Chevalley” of connected affine supergroups associated with Lie superalgebras of type D(2,1;a), for any possible value of the parameter a. This extends the results in [R. Fioresi, F. Gavarini, Chevalley Supergroups, Memoirs AMS 215 (2012), no. 1014] (and [R. Fioresi, F. Gavarini, On the construction of Chevalley supergroups, Supersymmetry in Mathematics & Physics (UCLA Los Angeles, U.S.A. 2010), 101–123, Lecture Notes in Mathematics 2027, Springer-Verlag, Berlin-Heidelberg, 2011]) where all other simple Lie superalgebras of classical type were considered. The case of simple Lie superalgebras of Cartan type being dealt with in [F. Gavarini, Algebraic supergroups of Cartan type, Forum Mathematicum (to appear), 92 pages], so this work completes the program of constructing connected affine supergroups associated with any simple Lie superalgebra.

Gavarini, F. (2014). Chevalley supergroups of type D(2,1;a). PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 57(2), 465-491 [10.1017/S0013091513000503].

Chevalley supergroups of type D(2,1;a)

GAVARINI, FABIO
2014-06-01

Abstract

We present a construction “a` la Chevalley” of connected affine supergroups associated with Lie superalgebras of type D(2,1;a), for any possible value of the parameter a. This extends the results in [R. Fioresi, F. Gavarini, Chevalley Supergroups, Memoirs AMS 215 (2012), no. 1014] (and [R. Fioresi, F. Gavarini, On the construction of Chevalley supergroups, Supersymmetry in Mathematics & Physics (UCLA Los Angeles, U.S.A. 2010), 101–123, Lecture Notes in Mathematics 2027, Springer-Verlag, Berlin-Heidelberg, 2011]) where all other simple Lie superalgebras of classical type were considered. The case of simple Lie superalgebras of Cartan type being dealt with in [F. Gavarini, Algebraic supergroups of Cartan type, Forum Mathematicum (to appear), 92 pages], so this work completes the program of constructing connected affine supergroups associated with any simple Lie superalgebra.
giu-2014
Pubblicato
Rilevanza internazionale
Articolo
Esperti anonimi
Settore MAT/02 - ALGEBRA
Settore MAT/03 - GEOMETRIA
English
Con Impact Factor ISI
supergroups; Lie superalgebras
http://journals.cambridge.org/action/displayJournal?jid=PEM
Gavarini, F. (2014). Chevalley supergroups of type D(2,1;a). PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 57(2), 465-491 [10.1017/S0013091513000503].
Gavarini, F
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2108/85348
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