Journal of Lie Theory 20 (2010), No. 1, 049--063
Copyright Heldermann Verlag 2010
On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal
Céline Righi
Dip. di Matematica, Istituto G. Castelnuovo, Università di Roma "La Sapienza", Piazzale Aldo Moro 5, 00185 Rome, Italy
righi@mat.uniroma1.it
Rupert W. T. Yu
Dép. de Mathématiques, Université de Poitiers, Téléport 2 - BP 30179, Blvd Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France
yuyu@math.univ-poitiers.fr
We give upper bounds for the index of the quotient of a Borel subalgebra of a simple Lie algebra or its nilpotent radical by an ad-nilpotent ideal. For the nilpotent radical quotient, our bound is a generalization of the formula for the index given by Panov in the type A case. In general, this bound is not exact. Using results of Panov ["On the index of certain nilpotent Lie algebras", J. of Math. Sci. 161 (2009) 122--129], we show that the upper bound for the Borel quotient is exact in the type A case, and we conjecture that it is exact in general.
Keywords: Index, Borel subalgebras, ad-nilpotent ideals.
MSC: 17B08, 17B20, 17B22
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