Representation Theory

ISSN 1088-4165

 

 

An averaging process for unipotent group actions


Author: Amnon Yekutieli
Journal: Represent. Theory 10 (2006), 147-157
MSC (2000): Primary 14L30; Secondary 18G30, 20G15
Published electronically: March 9, 2006
MathSciNet review: 2219110
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We present an averaging process for sections of a torsor under a unipotent group. This process allows one to integrate local sections of such a torsor into a global simplicial section. The results of this paper have applications to deformation quantization of algebraic varieties.


References [Enhancements On Off] (What's this?)

  • [Bo] Raoul Bott, Lectures on characteristic classes and foliations, Lectures on algebraic and differential topology (Second Latin American School in Math., Mexico City, 1971) Springer, Berlin, 1972, pp. 1–94. Lecture Notes in Math., Vol. 279. Notes by Lawrence Conlon, with two appendices by J. Stasheff. MR 0362335
  • [GK] I.M. Gelfand and D.A. Kazhdan, Some problems of differential geometry and the calculation of cohomologies of Lie algebras of vector fields, Soviet Math. Dokl. 12 (1971), no. 5, 1367-1370.
  • [Ho] Gerhard P. Hochschild, Basic theory of algebraic groups and Lie algebras, Graduate Texts in Mathematics, vol. 75, Springer-Verlag, New York-Berlin, 1981. MR 620024
  • [HY] Reinhold Hübl and Amnon Yekutieli, Adelic Chern forms and applications, Amer. J. Math. 121 (1999), no. 4, 797–839. MR 1704478
  • [Ko] Maxim Kontsevich, Deformation quantization of Poisson manifolds, Lett. Math. Phys. 66 (2003), no. 3, 157–216. MR 2062626, 10.1023/B:MATH.0000027508.00421.bf
  • [Ye] Amnon Yekutieli, Deformation quantization in algebraic geometry, Adv. Math. 198 (2005), no. 1, 383–432. MR 2183259, 10.1016/j.aim.2005.06.009

Similar Articles

Retrieve articles in Representation Theory of the American Mathematical Society with MSC (2000): 14L30, 18G30, 20G15

Retrieve articles in all journals with MSC (2000): 14L30, 18G30, 20G15


Additional Information

DOI: http://dx.doi.org/10.1090/S1088-4165-06-00285-8
Keywords: Unipotent group, torsor, simplicial set
Received by editor(s): May 11, 2005
Received by editor(s) in revised form: January 3, 2006
Published electronically: March 9, 2006
Additional Notes: This work was partially supported by the US – Israel Binational Science Foundation
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.