On the General Classification of Lie Bialgebra Structures over Polynomials

Abstract

The present article is a continuation of [5], where Lie bialgebra structures on 𝔤[u] were studied. These structures fall into different classes labelled by the vertices of the extended Dynkin diagram of 𝔤. In [5] the Lie bialgebras corresponding to − α_max were classified. In the present article, we investigate the Lie bialgebras corresponding to an arbitrary simple root α.

Key Words:

• Admissible triple
• Lagrangian subalgebra
• Lie bialgebra
• Parabolic subalgebra

2010 Mathematics Subject Classification:

• Primary: 17B37, 17B62
• Secondary: 17B81

ACKNOWLEDGMENT

The authors are indebted to the referee for useful recommendations and corrections for the final version of the article.

Notes

Communicated by M. Cohen.