Root systems extended by an abelian group and their Lie algebras
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 (Br, G)-graded Lie algebras
and as a special case, Lie G-tori of type Br,
are classified for r>2.
(To appear in Journal of Lie Theory)
Y. Yoshii < yoshii@math.usask.ca >