Burgdorf, SabineKlep, Igor2013-02-272013-02-272013-02-272012https://infoscience.epfl.ch/handle/20.500.14299/89784WOS:000309484800007We present tracial analogs of the classical results of Curto and Fialkow on moment matrices. A sequence of real numbers indexed by words in noncommuting variables with values invariant under cyclic permutations of the indexes, is called a tracial sequence. We prove that such a sequence can be represented with tracial moments of matrices if its corresponding moment matrix is positive semidefinite and of finite rank. A truncated tracial sequence allows for such a representation if and only if one of its extensions admits a flat extension. Finally, we apply this theory via duality to investigate trace-positive polynomials in noncommuting variables.(Truncated) moment problemnoncommutative polynomialsum of hermitian squaresmoment matrixfree positivitytext::journal::journal article::research article