2014/06/14 by Anton Izosimov, Izosimov, Anton
Chemistry · Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Carbohydrate Chemistry and Synthesis #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #math.RT
paper · pdf · doi:10.48550/arxiv.1406.3777
openalex publication_date 2014/06/14 · arxiv created 2014/07/07 · arxiv updated 2014/07/09 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
The Mischenko-Fomenko argument shift method allows to construct commutative subalgebras in the symmetric algebra S(\mathfrak g) of a finite-dimensional Lie algebra \mathfrak g. For a wide class of Lie algebras, these commutative subalgebras appear to be complete, i.e. they have maximal transcendence degree. However, for many algebras, Mischenko-Fomenko subalgebras are incomplete or even empty. In this case, we suggest a natural way how to extend Mischenko-Fomenko subalgebras, and give a completeness criterion for these extended subalgebras.