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Computational Invariant Theory pp 153–264Cite as

Invariant Theory of Infinite Groups

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Abstract

Throughout this section G will be a linearly reductive group over an algebraically closed field K and V will be an n-dimensional rational representation. We will present an algorithm for computing generators of the invariant ring K[V ]G (see Derksen [1]). This algorithm is actually quite simple and it is easy to implement. The essential step is just one Gröbner basis computation. We will also need the Reynolds operator. For now, the Reynolds operator \(\mathcal{R}\) is just a black box which has the required properties (see Definition 2.2.2). In Sect. 4.5 we will study how to compute the Reynolds operator for several examples of linearly reductive groups.

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Authors and Affiliations

  1. Department of Mathematics, University of Michigan, Ann Arbor, MI, USA

    Harm Derksen

  2. Zentrum Mathematik - M11, Technische Universität München, Garching, Germany

    Gregor Kemper

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  1. Harm Derksen
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  2. Gregor Kemper
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Derksen, H., Kemper, G. (2015). Invariant Theory of Infinite Groups. In: Computational Invariant Theory. Encyclopaedia of Mathematical Sciences. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48422-7_4

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