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Relatively free invariant algebras of finite reflection groups


Author: Mátyás Domokos
Journal: Trans. Amer. Math. Soc. 348 (1996), 2217-2234
MSC (1991): Primary 16W20; Secondary 16R10
DOI: https://doi.org/10.1090/S0002-9947-96-01687-X
MathSciNet review: 1363010
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Abstract: Let $G$ be a finite subgroup of $Gl_{n}(K)$ $(K$ is a field of characteristic $0$ and $n\geq 2)$ acting by linear substitution on a relatively free algebra $K\langle x_{1},\hdots ,x_{n}\rangle /I$ of a variety of unitary associative algebras. The algebra of invariants is relatively free if and only if $G$ is a pseudo-reflection group and $I$ contains the polynomial $[[x_{2},x_{1}],x_{1}].$


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Additional Information

Mátyás Domokos
Affiliation: Mathematical Institute of the Hungarian Academy of Sciences, P.O.B. 127, H-1364, Budapest, Hungary
Email: domokos@math-inst.hu

DOI: https://doi.org/10.1090/S0002-9947-96-01687-X
Keywords: Relatively free algebra, reflection group, invariants, Hilbert series
Received by editor(s): September 7, 1994
Additional Notes: This research was partially supported by Széchenyi István Scholarship Foundation and by Hungarian National Foundation for Scientific Research grant no. T4265.
Article copyright: © Copyright 1996 American Mathematical Society

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