Geodesic
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 Cet article a éte moissonné depuis la source Heldermann Verlag

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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 
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     author = {C. Righi and R. W. T. Yu },
     title = {On the {Index} of the {Quotient} of a {Borel} {Subalgebra} by an {ad-Nilpotent} {Ideal}},
     journal = {Journal of Lie theory},
     pages = {49--63},
     year = {2010},
     volume = {20},
     number = {1},
     url = {http://geodesic.mathdoc.fr/item/JLT_2010_20_1_JLT_2010_20_1_a4/}
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C. Righi; R. 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/JLT_2010_20_1_JLT_2010_20_1_a4/