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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
##### Keywords:
reductive group; freeness of invariant polynomials; slice
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