Summary: This paper is devoted to the construction and analysis of the Wigner functions for noncommutative quantum mechanics, their marginal distributions, and star-products, following a technique developed earlier, viz, using the unitary irreducible representations of the group \(\operatorname{G}_{\mathrm{NC}}\), which is the three fold central extension of the abelian group of \(\mathbb{R}^{4}\). These representations have been exhaustively studied in earlier papers. The group \(\operatorname{G}_{\mathrm{NC}}\) is identified with the kinematical symmetry group of noncommutative quantum mechanics of a system with two degrees of freedom. The Wigner functions studied here reflect different levels of non-commutativity – both the operators of position and those of momentum not commuting, the position operators not commuting and finally, the case of standard quantum mechanics, obeying the canonical commutation relations only. {
©2015 American Institute of Physics}