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

SN - 1083-4362

JO - Transformation Groups

JF - Transformation Groups

ER -