Actions of linearly reductive groups on affine PI algebras

DOI10.1090/memo/0414zbMath0691.16025OpenAlexW2091819491MaRDI QIDQ3032434

Nikolaus Vonessen

Publication date: 1989

Published in: Memoirs of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/memo/0414

zbMATH Keywords

inner automorphismsAzumaya algebrapolynomial identityrational actionfixed ringlinearly reductive groupstotal ring of fractionslying overfinitely generated k-algebraaffine prime Noetherian PI-algebra

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Automorphisms and endomorphisms (16W20) Vector and tensor algebra, theory of invariants (15A72) Separable algebras (e.g., quaternion algebras, Azumaya algebras, etc.) (16H05) Localization and associative Noetherian rings (16P50) Rings with polynomial identity (16Rxx) Modules, bimodules and ideals in associative algebras (16Dxx)

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Group actions on central simple algebras: a geometric approach., Group actions and invariants in algebras of generic matrices., Rationality of Hilbert series in noncommutative invariant theory, Unnamed Item, Actions of solvable algebraic groups on central simple algebras., Integrality for PI-rings, Classical invariant theory for free metabelian Lie algebras, Actions of Linearly Reductive Groups on Pi-Algebras, Actions of algebraic groups on the spectrum of rational ideals. II, A Hilbert-Nagata theorem in noncommutative invariant theory, Constants of Weitzenböck derivations and invariants of unipotent transformations acting on relatively free algebras.