On the correspondence of Affine Generalized Root Systems and symmetrizable affine Kac-Moody superalgebras

2015/07/26 by Shaviv, Ary
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1507.07174

Abstract

Generalized root systems (GRS), that were introduced by V. Serganova, are a generalization of finite root systems (RS). We define a generalization of affine root systems (ARS), which we call affine generalized root systems (AGRS). The set of real roots of almost every symmetrizable affine indecomposable Kac-Moody superalgebra is an irreducible AGRS. In this paper we classify all AGRSs and show that almost every irreducible AGRS is the set of real roots of a symmetrizable affine indecomposable Kac-Moody superalgebra.

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