Graded differential geometry of graded matrix algebras

@article{Grosse1999GradedDG,
  title={Graded differential geometry of graded matrix algebras},
  author={Harald Grosse and Gert Reiter},
  journal={Journal of Mathematical Physics},
  year={1999},
  volume={40},
  pages={6609-6625}
}
We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)×(n+m)-matrices with the “usual block matrix grading” (for n≠m). Beside the (infinite-dimensional) algebra of graded forms, the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and curvature are introduced and investigated. In particular we prove the universality of the graded derivation-based first-order differential calculus… 

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