Deformations of schemes and other bialgebraic structures

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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.
Original languageEnglish
Pages (from-to)1601-1629
Number of pages29
JournalTransactions of the American Mathematical Society
Volume360
Issue number3
DOIs
Publication statusPublished - 1 Mar 2008

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