Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 14, No. 2, pp. 427--441 (2004)

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Root Systems Extended by an Abelian Group and Their Lie Algebras

Yoji Yoshii

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

Abstract: 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 $(\Delta,G)$-graded Lie algebras have such root systems. Finally, division $({\rm B}_l,G)$-graded Lie algebras and as a special case, Lie $G$-tori of type ${rm B}_l$, are classified for $l\geq 3$. \hfill\break {\eightsl 2000 MSC:} Primary 17B65;\quad secondary 17C50 \hfill\break {\eightsl Keywords:} extended affine root systems; Jordan tori

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