Remarks on generalized Fedosov algebras

The variant of Fedosov construction based on fairly general fiberwise product in the Weyl bundle is studied. We analyze generalized star products of functions, of sections of endomorphisms bundle, and those generating deformed bimodule structure as introduced previously by Waldmann. Isomorphisms of generalized Fedosov algebras are considered and their relevance for deriving Seiberg-Witten map is described. The existence of the trace functional is established. Explicit expressions for star products and the trace functional are provided up to the second power of deformation parameter. The example of symmetric part of noncommutativity tensor is discussed as a case with possible field-theoretic application.