Geodesic
On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal
Céline Righi1 ; Rupert W. T. Yu2
1Dip. di Matematica, Istituto G. Castelnuovo, Università di Roma "La Sapienza", Piazzale Aldo Moro 5, 00185 Rome, Italy
2Dép. de Mathématiques, Université de Poitiers, Téléport 2 - BP 30179, Blvd Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France
Journal of Lie Theory, Tome 20 (2010) no. 1, pp. 49-63

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 17B08, 17B20, 17B22
Mots-clés : Index, Borel subalgebras, ad-nilpotent ideals

Céline Righi  1   ; Rupert W. T. Yu  2

1 Dip. di Matematica, Istituto G. Castelnuovo, Università di Roma "La Sapienza", Piazzale Aldo Moro 5, 00185 Rome, Italy
2 Dép. de Mathématiques, Université de Poitiers, Téléport 2 - BP 30179, Blvd Marie et Pierre Curie, 86962 Futuroscope Chasseneuil, France 
Céline Righi; Rupert W. T. Yu. On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal. Journal of Lie Theory, Tome 20 (2010) no. 1, pp. 49-63. http://geodesic.mathdoc.fr/item/JOLT_2010_20_1_a4/
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