Jump to ContentJump to Main Navigation
Geometry and Physics: Volume IA Festschrift in honour of Nigel Hitchin$
Users without a subscription are not able to see the full content.

Andrew Dancer, Jørgen Ellegaard Andersen, and Oscar García-Prada

Print publication date: 2018

Print ISBN-13: 9780198802013

Published to Oxford Scholarship Online: December 2018

DOI: 10.1093/oso/9780198802013.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2019. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 19 July 2019

Deformation Theory of Lie Bialgebra Properads

Deformation Theory of Lie Bialgebra Properads

Chapter:
(p.219) 10 Deformation Theory of Lie Bialgebra Properads
Source:
Geometry and Physics: Volume I
Author(s):

Sergei Merkulov

Thomas Willwacher

Publisher:
Oxford University Press
DOI:10.1093/oso/9780198802013.003.0010

This chapter presents the homotopy derivations of the properads governing even and odd Lie bialgebras, as well as involutive Lie bialgebras. The answer may be expressed in terms of the Kontsevich graph complexes. In particular, this shows that the Grothendieck–Teichmuller group acts faithfully and essentially transitively on the completions of the properads governing even Lie bialgebras and involutive Lie bialgebras, up to homotopy. This shows also that, in contrast to the even case, the properad governing odd Lie bialgebras admits precisely one non-trivial automorphism—the standard rescaling automorphism, and that it has precisely one non-trivial deformation, which we describe explicitly.

Keywords:   properad, Lie bialgebra, graph complex, homotopy derivation, deformation

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .