Note on the extended noncommutativity of coordinates

We present in this short note an idea about a possible extension of the standard noncommutative algebra to the formal differential operators framework. In this sense, we develop an analysis and derive an extended noncommutative algebra given by [xa, xb]*=i(θ+χ)ab where θab, is the standard noncommutative parameter and χab(x)≡χabμ(x)δμ=1/2(xaθμb-xbθa)δμ is an antisymmetric non-constant vector-field shown to play the role of the extended deformation parameter. This idea was motivated by the importance of noncommutative geometry framework in the current subject of D-brane and matrix theory physics. (author)