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On non-connected simple linear groups with a free algebra of invariants. (English. Russian original) Zbl 0893.14017
Izv. Math. 60, No. 4, 811-856 (1996); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 60, No. 4, 159-204 (1996).
Let \(V\) be a finite dimensional vector space over \(\mathbb{C}\) and \(G\) a semisimple algebraic subgroup of \(\text{GL}(V)\). The author gives a criterion for coregularity of \(G\) (i.e., for freeness of the algebra of \(G\)-invariant polynomials on \(V\)) in terms of the action of \(G/G^0\) on \(V/ /G^0\). All connected noncoregular simple linear algebraic groups having a finite coregular extension are classified and all such extensions in each case are described.
Reviewer: V.L.Popov (Moskva)

MSC:
14L40 Other algebraic groups (geometric aspects)
13A50 Actions of groups on commutative rings; invariant theory
20G05 Representation theory for linear algebraic groups
14L24 Geometric invariant theory
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