Polynomial Lie algebras

V. M. Buchstaber, D. V. Leykin

Research output: Contribution to journalArticlepeer-review

28 Citations (Scopus)


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,..., 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.

Original languageEnglish
Pages (from-to)267-280
Number of pages14
JournalFunctional Analysis and its Applications
Issue number4
Publication statusPublished - 2002
Externally publishedYes


  • Co-algebra
  • Convolution of invariants
  • Lie algebra
  • Moving frames


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