| The last version of the lecture notes, as of 8th July 2018, can be found here. These are introductory lecture notes to Dirac and generalized geometry. They reflect the contents of this course and are better understood as accompanying material to the lectures. |
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Basic references
[FO17] Jose Figueroa-O'Farrill. Spin geometry. Lecture notes, 2017. Available online.
[Gar11] D. J. H. Garling. Cli ord algebras: an introduction, volume 78 of London Mathematical Society Student Texts. Cambridge University Press, Cambridge, 2011.
[Gre78] Werner Greub. Multilinear algebra. Springer-Verlag, New York- Heidelberg, second edition, 1978. Available online from Weizmann network.
[Rom08] Steven Roman. Advanced linear algebra, volume 135 of Graduate Texts in Mathematics. Springer, New York, third edition, 2008. Available online from Weizmann network. Look at the beginning of Chapters 1, 9 and 11.
More references can be found in the lecture notes.
Background material
[Gua04] Marco Gualtieri. Generalized complex geometry. arXiv:math/0401221, January 2004. Available online.
[Gua11] Marco Gualtieri. Generalized complex geometry. Ann. of Math. (2), 174(1):75--123, 2011. Available online.
[Hit03] Nigel Hitchin. Generalized Calabi-Yau manifolds. Q. J. Math., 54(3):281--308, 2003. Available online.
Finally, these lecture notes are also very interesting:[Hit10b] Nigel Hitchin. Lectures on generalized geometry. arXiv:math.DG:1008.0973, August 2010. Available online.