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On algebras of invariants and codimension 1 Luna strata for nonconnected groups. (English) Zbl 1035.14018
Summary: In order to describe explicitly the algebra of invariants for a non-connected reductive subgroup \(G\subseteq GL(V)\) we apply the method of strata. For this we describe codimension 1 strata of the quotient \(V//G\) and study the normality property of their closures. We find some criteria for \({\mathbf k}[V]^G\) to be polynomial or a hypersurface. Then we apply these results to complete the classification [see D. A. Shmel’kin, Izv. Math. 60, 811–856 (1996; Zbl 0893.14017)] of nonconnected simple groups \(G\) such that \({\mathbf k}[V]^G\) is polynomial.

MSC:
14L30 Group actions on varieties or schemes (quotients)
20G05 Representation theory for linear algebraic groups
13A50 Actions of groups on commutative rings; invariant theory
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