The bar automorphism in quantum groups and geometry of quiver representations

The bar automorphism in quantum groups and geometry of quiver representations

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 prov...

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Veröffentlicht in:Annales de l'Institut Fourier 2006, Vol.56 (1), p.255-267
Hauptverfasser: CALDERO, Philippe, REINEKE, Markus
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algebraic Geometry
Exact sciences and technology
Mathematics
Nonassociative rings and algebras
Representation Theory
Sciences and techniques of general use
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Zusammenfassung: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.
ISSN:0373-0956
1777-5310
DOI:10.5802/aif.2179