Journal of Lie TheoryVol. 14, No. 2, pp. 427--441 (2004)
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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 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.
© 2004 Heldermann Verlag
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