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- Title
Double Lie algebroids and representations up to homotopy.
- Authors
Gracia-Saz, A.; Jotz Lean, M.; Mackenzie, K. C. H.; Mehta, R. A.
- Abstract
We show that a double Lie algebroid, together with a chosen decomposition, is equivalent to a pair of 2-term representations up to homotopy satisfying compatibility conditions which extend the notion of matched pair of Lie algebroids. We discuss in detail the double Lie algebroids arising from the tangent bundle of a Lie algebroid and the cotangent bundle of a Lie bialgebroid.
- Subjects
LIE algebroids; REPRESENTATION theory; HOMOTOPY theory; MATHEMATICAL decomposition; MATHEMATICAL analysis
- Publication
Journal of Homotopy & Related Structures, 2018, Vol 13, Issue 2, p287
- ISSN
2193-8407
- Publication type
Article
- DOI
10.1007/s40062-017-0183-1