Q-Manifolds and Mackenzie Theory

    Research output: Contribution to journalArticlepeer-review


    Double Lie algebroids were discovered by Kirill Mackenzie from the study of double Lie groupoids and were defined in terms of rather complicated conditions making use of duality theory for Lie algebroids and double vector bundles. In this paper we establish a simple alternative characterization of double Lie algebroids in a supermanifold language. Namely, we show that a double Lie algebroid in Mackenzie's sense is equivalent to a double vector bundle endowed with a pair of commuting homological vector fields of appropriate weights. Our approach helps to simplify and elucidate Mackenzie's original definition; we show how it fits into a bigger picture of equivalent structures on 'neighbor' double vector bundles. It also opens ways for extending the theory to multiple Lie algebroids, which we introduce here. © 2012 Springer-Verlag.
    Original languageEnglish
    Pages (from-to)279-310
    Number of pages31
    JournalCommunications in Mathematical Physics
    Issue number2
    Publication statusPublished - Oct 2012


    Dive into the research topics of 'Q-Manifolds and Mackenzie Theory'. Together they form a unique fingerprint.

    Cite this