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Jordan-Kronecker invariants of Lie algebra representations and degrees of invariant polynomials

journal contribution
posted on 12.01.2021, 09:20 by Alexey Bolsinov, Anton Izosimov, Ivan Kozlov
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.

Funding

Russian Science Foundation, project No.17-11-01303

NSF grant DMS-2008021

History

School

  • Science

Department

  • Mathematical Sciences

Published in

Transformation Groups

Publisher

Springer Verlag

Version

AM (Accepted Manuscript)

Publisher statement

This is a post-peer-review, pre-copyedit version of an article published in Transformation Groups. The final authenticated version is available online at: http://dx.doi.org/[insert DOI].

Acceptance date

13/12/2020

ISSN

1083-4362

eISSN

1531-586X

Language

en

Depositor

Dr Alexey Bolsinov. Deposit date: 10 January 2021

Exports

Loughborough Publications

Categories

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