Remarks on the star product of functions on finite and compact groups

We show that the characters χ(g1g2g3−1) of irreducible unitary representations of finite groups and compact Lie groups provide kernels of star-product on complex valued functions f(g)f(g) of the group elements g  . Examples of permutation groups of two and three elements as well as SU(2)SU(2) group are considered. The k-deformed star products of the functions of finite and compact Lie groups are presented. The explicit form of the quantizers and dequantizers as well as the duality symmetry of the considered star products of the functions on the finite and compact Lie groups are discussed.