Some remarks about Mishchenko-Fomenko subalgebras

2014/05/07 by Alexey Bolsinov, Bolsinov, Alexey
Mathematics · #15A21 #15A22 #17B45 #17B80 #37J35 #53D17 #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:15A21 #msc:15A22 #msc:17B45 #msc:17B80 #msc:37J35 #msc:53D17

paper · pdf · doi:10.48550/arxiv.1405.1710

arxiv created 2014/05/07 · arxiv updated 2014/05/08

Abstract

We discuss and compare two different approaches to the notion of Mishchenko--Fomenko subalgebras in Poisson-Lie algebras of finite-dimensional Lie algebras. One of them, commonly accepted by the algebraic community, uses polynomial \Ad^*-invariants. The other is based on formal \Ad^*-invariants and allows one to deal with arbitrary Lie algebras, not necessarily algebraic. In this sense, the latter is more universal.

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