TY - JOUR
T1 - JORDAN–KRONECKER INVARIANTS OF LIE ALGEBRA REPRESENTATIONS AND DEGREES OF INVARIANT POLYNOMIALS
AU - Bolsinov, A.
AU - Izosimov, A.
AU - Kozlov, I.
N1 - Funding Information:
A. Izosimov is supported by NSF grant DMS-2008021.
Funding Information:
A. Bolsinov is supported by the Russian Science Foundation, project No.17-11-01303.
Publisher Copyright:
© 2021, The Author(s).
PY - 2021
Y1 - 2021
N2 - 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.
AB - 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.
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U2 - 10.1007/s00031-021-09661-0
DO - 10.1007/s00031-021-09661-0
M3 - Article
AN - SCOPUS:85108176607
JO - Transformation Groups
JF - Transformation Groups
SN - 1083-4362
ER -