Twisted exterior derivatives for enveloping algebras

Details Twisted exterior derivatives for enveloping algebras Twisted exterior derivatives for enveloping algebras

2008-06-05

arxiv.org/abs/0806.0978v1

Mathematics

Quantum Algebra

7 pages

Scientific paper

We extend the representations of finite-dimensional Lie algebra by derivations of the completed symmetric algebra of its dual to the derivations of a bigger algebra which includes the exterior algebra on the Lie algebra. This enables a construction of a twisted version of the exterior differential calculus with the enveloping algebra in the role of the coordinate algebra. In this twisted version, the commutators between 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 Leibniz rule is deformed.

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