Geodesic
Polynomial Lie Algebras
Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 18-34

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We introduce and study a special class of infinite-dimensional Lie algebras that are finite-dimensional modules over a ring of polynomials. The Lie algebras of this class are said to be polynomial. Some classification results are obtained. An associative co-algebra structure on the rings $k[x_1,\dots,x_n]/(f_1,\dots,f_n)$ is introduced and, on its basis, an explicit expression for convolution matrices of invariants for isolated singularities of functions is found. The structure polynomials of moving frames defined by convolution matrices are constructed for simple singularities of the types $A$, $B$, $C$, $D$, and $E_6$.
Keywords: Lie algebra, moving frame, co-algebra.
Mots-clés : convolution of invariants 
@article{FAA_2002_36_4_a1,
     author = {V. M. Buchstaber and D. V. Leikin},
     title = {Polynomial {Lie} {Algebras}},
     journal = {Funkcionalʹnyj analiz i ego prilo\v{z}eni\^a},
     pages = {18--34},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2002},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a1/}
}
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V. M. Buchstaber; D. V. Leikin. Polynomial Lie Algebras. Funkcionalʹnyj analiz i ego priloženiâ, Tome 36 (2002) no. 4, pp. 18-34. http://geodesic.mathdoc.fr/item/FAA_2002_36_4_a1/