ASSOCIATIVITY and INTEGRABILITY

Rui Loja Fernandes, Daan Michiels

Research output: Contribution to journalArticlepeer-review

Abstract

We provide a complete solution to the problem of extending a local Lie groupoid to a global Lie groupoid. First, we show that the classical Mal’cev’s theorem, which characterizes local Lie groups that can be extended to global Lie groups, also holds in the groupoid setting. Next, we describe a construction that can be used to obtain any local Lie groupoid with integrable algebroid. Last, our main result establishes a precise relationship between the integrability of a Lie algebroid and the failure in associativity of a local integration. We give a simplicial interpretation of this result showing that the monodromy groups of a Lie algebroid manifest themselves combinatorially in a local integration, as a lack of associativity.

Original languageEnglish (US)
Pages (from-to)5057-5110
Number of pages54
JournalTransactions of the American Mathematical Society
Volume373
Issue number7
DOIs
StatePublished - Jul 2020

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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