• 1
  • 1
  • 6
  • 5
  • 6
  • 3
  • 4

“School of Physic”

Back to Papers Home
Back to Papers of School of Physic

Paper   IPM / Physic / 7143
School of Physics
  Title:   Dirac Structures on Modules 1
  Author(s):  A. Shafei Deh Abad
  Status:   Preprint
  Journal:
  No.:  0
  Year:  1998
  Supported by:  IPM
  Abstract:
In this paper we give a simple definition of Dirac structures on modules and on vector bundles which includes the existing ones, and complex structures on vector bundles, as special cases. Among other thing we prove:
1) Each two Dirac structures on a (Hermitian) module M are (isometrically) isomorphic(Hermitian) modules. Moreover, the set of all Dirac structures on Mis in one-to-one correspondence with Aut(M).
2) Let M be a smooth manifold, and let η be a (Hermitian) vector bundle over M. Then, to each Dirac structure on η, there corresponds a unique Dirac structure on the (Hermitian) C(M)−module of its sections. Conversely, to each Dirac structure on a Hermitian finitely generated projective C(M)−module there corresponds a unique Dirac structure on the associated (Hermitian) vector bundle over M.
3) Let M be a Hilbert R-module. Then to each Dirac structure on Mand to each state of R there corresponds a unique Dirac structure on the associated Hilbert space.

Download TeX format
back to top
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
Clients Logo
scroll left or right