Functional Analysis and Its Applications

, Volume 36, Issue 4, pp 267–280

Polynomial Lie Algebras

  • V. M. Buchstaber
  • D. V. Leykin

DOI: 10.1023/A:1021757609372

Cite this article as:
Buchstaber, V.M. & Leykin, D.V. Functional Analysis and Its Applications (2002) 36: 267. doi:10.1023/A:1021757609372


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[x1,...,xn]/(f1,...,fn) 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 E6.

Lie algebra, moving frame, convolution of invariants, co-algebra 

Copyright information

© Plenum Publishing Corporation 2002

Authors and Affiliations

  • V. M. Buchstaber
  • D. V. Leykin

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