Open Access
Article
Representation up to homotopy of double algebroids and their transgression classes
*S. MeratiCorresponding authors.merati@shirazuac.irDepartment of MathematicsCollege of SciencesShiraz UniversityShiraz, P.O. Box 71457-44776, IranView full profile → , M. R. Farhangdoostfarhang®shirazu.ac.irDepartment of MathematicsCollege of SciencesShiraz UniversityShiraz, P.O. Box 71457-44776, IranView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Jul 2017
- Accepted:
- 21 Nov 2017
- Published Online:
- 12 Jun 2018
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2018.1436269
- Pages:
- 89–99
Abstract
In this work, we present definition of the representation of double Lie algebroids and find a one-to-one correspondence to introduce representation up to homotopy of double Lie algebroids and gauge equivalence of them. Also dual, tensor product and direct sum representations up to homotopy are made as a double Lie algebroid modules. We conclude this paper by generalization of some Lie algebroid oo-representation properties to oo-representation of double Lie algebroids and introduce transgression classes for double Lie algebroids.
Keywords
Subject Classifications
53D1753C1253C05
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