• Corpus ID: 17657228

Twisted exterior derivatives for enveloping algebras

@inproceedings{vSkoda2008TwistedED,
  title={Twisted exterior derivatives for enveloping algebras},
  author={Zoran vSkoda},
  year={2008}
}

• Zoran vSkoda
• Published 5 June 2008
• Mathematics

Consider any representation φ of a finite-dimensional Lie algebra g by derivations of the completed symmetric algebra Ŝ(g) of its dual. Consider the tensor product of Ŝ(g∗) and the exterior algebra Λ(g). We show that the representation φ extends canonically to the representation φ̃ of that tensor product algebra. We construct an exterior derivative on that algebra, giving rise to a twisted version of the exterior differential calculus with the universal enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators between the noncommutative differentials and coordinates are formal power series in partial derivatives. The square of the corresponding exterior derivative is zero like in the classical case, but the graded Leibniz rule is deformed.