2014/07/07 by Alexey Bolsinov, Alexey V. Bolsinov, Bolsinov, Alexey +5
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #math.RT
paper · pdf · doi:10.48550/arxiv.1407.1878
18 pages
arxiv created 2019/11/28 · arxiv updated 2019/12/02
For an arbitrary representation ρ of a complex finite-dimensional Lie algebra, we construct a collection of numbers that we call the Jordan-Kronecker invariants of ρ. Among other interesting properties, these numbers provide lower bounds for degrees of polynomial invariants of ρ. Furthermore, we prove that these lower bounds are exact if and only if the invariants are independent outside of a set of large codimension. Finally, we show that under certain additional assumptions our bounds are exact if and only if the algebra of invariants is freely generated.