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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Deformations of schemes and other bialgebraic structures
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by J. P. Pridham PDF
Trans. Amer. Math. Soc. 360 (2008), 1601-1629 Request permission

Abstract:

There has long been a philosophy that every deformation problem in characteristic zero should be governed by a differential graded Lie algebra (DGLA). In this paper, we show how to construct a Simplicial Deformation Complex (SDC) governing any bialgebraic deformation problem. Examples of such problems are deformations of a Hopf algebra, or of an arbitrary scheme. In characteristic zero, SDCs and DGLAs are shown to be equivalent.
References
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Additional Information
  • J. P. Pridham
  • Affiliation: Trinity College, Cambridge, CB2 1TQ, United Kingdom
  • Email: J.P.Pridham@dpmms.cam.ac.uk
  • Received by editor(s): October 31, 2005
  • Received by editor(s) in revised form: April 25, 2006
  • Published electronically: July 23, 2007
  • Additional Notes: The author was supported during this research by Trinity College, Cambridge and by the Isle of Man Department of Education
  • © Copyright 2007 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 360 (2008), 1601-1629
  • MSC (2000): Primary 14B12, 14D15, 13D10
  • DOI: https://doi.org/10.1090/S0002-9947-07-04355-3
  • MathSciNet review: 2357707