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The additive group actions on -homology planes

Kayo Masuda, Masayoshi Miyanishi (2003)

Annales de l’institut Fourier

In this article, we prove that a -homology plane X with two algebraically independent G a -actions is isomorphic to either the affine plane or a quotient of an affine hypersurface x y = z m - 1 in the affine 3 -space via a free / m -action, where m is the order of a finite group H 1 ( X ; ) .

The bar automorphism in quantum groups and geometry of quiver representations

Philippe Caldero, Markus Reineke (2006)

Annales de l’institut Fourier

Two geometric interpretations of the bar automorphism in the positive part of a quantized enveloping algebra are given. The first is in terms of numbers of rational points over finite fields of quiver analogues of orbital varieties; the second is in terms of a duality of constructible functions provided by preprojective varieties of quivers.

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