Symmetrisation and the Feigin-Frenkel centre

2019/10/22 by Oksana Yakimova, Yakimova, Oksana · 2 citations
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1910.10204

Abstract

For simple Lie algebras of types B, C, and D, we provide new explicit formulas for the generators of the Feigin-Frenkel centre. These formulas make use of the symmetrisation map as well as some well-chosen symmetric invariants of \mathfrak g. There are some general results on the role of the symmetrisation map in the explicit description of the FF-centre. The advantage of our method is that it reduces questions about elements of the FF-centre to questions on the structure of the symmetric invariants in a type-free way. As an illustration, we deal with type G₂ by hand.

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