Geodesic
Lie Algebras of Simple Hypersurface Singularities
Journal of Lie theory, Tome 16 (2006) no. 4, pp. 621-649 Cet article a éte moissonné depuis la source Heldermann Verlag

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We investigate structural properties and numerical invariants of the finite-dimensional solvable Lie algebras naturally associated with simple hypersurface singularities. In particular, we establish that the analytic isomorphism class of a simple hypersurface singularity is determined by the Lie algebra of derivations of its moduli algebra if the dimension of the latter algebra is not less than 6. We also describe natural gradings on the Lie algebras of simple singularities and show that all roots of their Poincar� polynomials lie on the unit circle. Moreover, the indices of those Lie algebras are calculated and existence of maximal commutative polarizations is established.
Classification : 32S25, 17B30, 17B40
Mots-clés : Isolated hypersurface singularity, moduli algebra, derivation, vector field, index of Lie algebra, maximal commutative polarization 
@article{JLT_2006_16_4_JLT_2006_16_4_a1,
     author = {A. G. Elashvili and G. Khimshiashvili },
     title = {Lie {Algebras} of {Simple} {Hypersurface} {Singularities}},
     journal = {Journal of Lie theory},
     pages = {621--649},
     year = {2006},
     volume = {16},
     number = {4},
     url = {http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a1/}
}
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A. G. Elashvili; G. Khimshiashvili . Lie Algebras of Simple Hypersurface Singularities. Journal of Lie theory, Tome 16 (2006) no. 4, pp. 621-649. http://geodesic.mathdoc.fr/item/JLT_2006_16_4_JLT_2006_16_4_a1/