Abstract
The problem of finding generators of the subalgebra of invariants under the action of a group of automorphisms of a finite-dimensional Lie algebra on its universal enveloping algebra is reduced to finding homogeneous generators of the same group acting on the symmetric tensor algebra of the Lie algebra. This process is applied to prove a constructive Hilbert–Nagata Theorem (including degree bounds) for the algebra of invariants in a Lie nilpotent relatively free associative algebra endowed with an action induced by a representation of a reductive group.
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Mátyás Domokos is partially supported by the exchange program between the Hungarian and Bulgarian Academies of Sciences and by the Hungarian National Research, Development and Innovation Office, NKFIH K 119934.
Vesselin Drensky is partially supported by the exchange program between the Hungarian and Bulgarian Academies of Sciences and by Grant I02/18 of the Bulgarian National Science Fund.
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DOMOKOS, M., DRENSKY, V. CONSTRUCTIVE NONCOMMMUTATIVE INVARIANT THEORY. Transformation Groups 26, 215–228 (2021). https://doi.org/10.1007/s00031-021-09643-2
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DOI: https://doi.org/10.1007/s00031-021-09643-2