The Free Courant Algebroid
Differential Geometry
2014-07-29 v1 Category Theory
Rings and Algebras
Abstract
We introduce the category of generalized Courant algebroids and show that it admits a free object on any anchored vector bundle. The free Courant algebroid is built from two components: the generalized Courant algebroid associated to a symmetric Leibniz algebroid and the free symmetric Leibniz algebroid on an anchored vector bundle. Our construction is thus based on the new concept of symmetric Leibniz algebroid. We compare this subclass of Leibniz algebroids with the subclass of Loday algebroids that was introduced and studied in a previous paper of Grabowski, Khudaverdyan and Poncin.
Keywords
Cite
@article{arxiv.1407.7460,
title = {The Free Courant Algebroid},
author = {Benoit Jubin and Norbert Poncin and Kyousuke Uchino},
journal= {arXiv preprint arXiv:1407.7460},
year = {2014}
}
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25 pages