Journal of Lie Theory Vol. 14, No. 2, pp. 427441 (2004) 

Root Systems Extended by an Abelian Group and Their Lie AlgebrasYoji YoshiiYoji YoshiiDepartment of Mathematics and Statistics University of Saskatchewan 106 Wiggins Rd, Saskatoon, SK., S7N 5E6 Canada yoshii@math.usask.ca 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 Full text of the article:
Electronic version published on: 1 Sep 2004. This page was last modified: 1 Sep 2004.
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