Double Lie algebroids and representations up to homotopy

作者：Gracia Saz A; Lean M Jotz; Mackenzie K C H^*; Mehta R A

来源：Journal of Homotopy and Related Structures, 2018, 13(2): 287-319.

DOI：10.1007/s40062-017-0183-1

• Double Lie algebroids
• Representations up to homotopy
• Matched pairs

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.

• 出版日期2018-6