2026/07/27 by Nikita Safonkin
Mathematics · #math.QA #math.RA #math.RT
10 pages
arxiv created 2026/07/30 · arxiv updated 2026/08/03
We call a unital associative algebra A trace residually finite-dimensional if its elements are separated by finite-dimensional representations and its cocenter A/[A,A] is separated by the corresponding trace functionals. For RFD algebras A and B, we prove that the trace radical of A*B, the common kernel of all finite-dimensional trace functionals, is the direct sum of the trace radicals of A and B, which implies that A*B is trace RFD if and only if both A and B are trace RFD. The proof combines an explicit cocenter decomposition with a construction of finite-dimensional representations whose traces detect nonzero classes of words of length greater than one.