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This article is cited in 32 scientific papers (total in 33 papers)
Polynomial Lie Algebras
V. M. Buchstabera, D. V. Leikinb a Steklov Mathematical Institute, Russian Academy of Sciences
b Institute of Magnetism, National Academy of Sciences of Ukraine
Abstract:
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, convolution of invariants, co-algebra.
Received: 05.05.2002
Citation:
V. M. Buchstaber, D. V. Leikin, “Polynomial Lie Algebras”, Funktsional. Anal. i Prilozhen., 36:4 (2002), 18–34; Funct. Anal. Appl., 36:4 (2002), 267–280
Linking options:
https://www.mathnet.ru/eng/faa216https://doi.org/10.4213/faa216 https://www.mathnet.ru/eng/faa/v36/i4/p18
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