%0 Journal Article %1 Courant1990Dirac %A Courant, Theodore J. %D 1990 %J Transactions of the American Mathematical Society %K 47j35-nonlinear-evolution-equations 70h45-constrained-dynamics-diracs-theory-of-constraints %N 2 %P 631--661 %R 10.1090/s0002-9947-1990-0998124-1 %T Dirac Manifolds %U http://dx.doi.org/10.1090/s0002-9947-1990-0998124-1 %V 319 %X A Dirac structure on a vector space is a subspace of with a skew form on it. It is shown that these structures correspond to subspaces of satisfying a maximality condition, and having the property that a certain symmetric form on vanishes when restricted to them. Dirac structures on a vector space are analyzed in terms of bases, and a generalized Cayley transformation is defined which takes a Dirac structure to an element of . Finally a method is given for passing a Dirac structure on a vector space to a Dirac structure on any subspace.

@article{Courant1990Dirac, abstract = {{A Dirac structure on a vector space is a subspace of with a skew form on it. It is shown that these structures correspond to subspaces of satisfying a maximality condition, and having the property that a certain symmetric form on vanishes when restricted to them. Dirac structures on a vector space are analyzed in terms of bases, and a generalized Cayley transformation is defined which takes a Dirac structure to an element of . Finally a method is given for passing a Dirac structure on a vector space to a Dirac structure on any subspace.}}, added-at = {2019-03-01T00:11:50.000+0100}, author = {Courant, Theodore J.}, biburl = {https://www.bibsonomy.org/bibtex/282f9d7cc94ff9e47ec12682e77ee6012/gdmcbain}, citeulike-article-id = {14502701}, citeulike-attachment-1 = {courant_90_dirac.pdf; /pdf/user/gdmcbain/article/14502701/1124774/courant_90_dirac.pdf; 7589f0498d75465cc51ed3924f61de8b9d6884dc}, citeulike-linkout-0 = {http://dx.doi.org/10.1090/s0002-9947-1990-0998124-1}, doi = {10.1090/s0002-9947-1990-0998124-1}, file = {courant_90_dirac.pdf}, interhash = {b4c7c535faf9372846d9c900fc78ec6d}, intrahash = {82f9d7cc94ff9e47ec12682e77ee6012}, issn = {0002-9947}, journal = {Transactions of the American Mathematical Society}, keywords = {47j35-nonlinear-evolution-equations 70h45-constrained-dynamics-diracs-theory-of-constraints}, number = 2, pages = {631--661}, posted-at = {2017-12-13 23:52:57}, priority = {5}, timestamp = {2019-03-01T00:11:50.000+0100}, title = {{Dirac Manifolds}}, url = {http://dx.doi.org/10.1090/s0002-9947-1990-0998124-1}, volume = 319, year = 1990 }