Journal of Lie Theory

no. 1
On the Index of the Quotient of a Borel Subalgebra by an ad-Nilpotent Ideal
Journal of Lie Theory, Volume 20 (2010) no. 1, pp. 49-63
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.
DOI: 10.5802/jolt.586
Classification: 17B08, 17B20, 17B22
Keywords: 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},
     doi = {10.5802/jolt.586},
     zbl = {1237.17015},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.586/}
}
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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, Volume 20 (2010) no. 1, pp. 49-63. doi: 10.5802/jolt.586

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