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Journal of Lie Theory 14 (2004), No. 2, 371--394
Copyright Heldermann Verlag 2004

Root Systems Extended by an Abelian Group and their Lie Algebras

Yoji Yoshii
Dept. of Mathematics and Statistics, University of Saskatchewan, 106 Wiggins Rd, Saskatoon SK, S7N 5E6 Canada,

We introduce the notion of a root system extended by an abelian group G. This concept generalizes extended affine root systems. We classify them in terms of (translated) reflection spaces of G. Then we see that division (Δ, G)-graded Lie algebras have such root systems. Finally, division (Bl , G)-graded Lie algebras and as a special case, Lie G-tori of type Bl , are classified for l ≥ 3.

Keywords: extended affine root systems, Jordan tori.

MSC 2000: 17B65; 17C50.

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