We find an infinite dimensional free algebra which lives at large N in any
SU(N)-invariant action or Hamiltonian theory of bosonic matrices. The natural
basis of this algebra is a free-algebraic generalization of Chebyshev
polynomials and the dual basis is closely related to the planar connected
parts. This leads to a number of free-algebraic forms of the master field
including an algebraic derivation of the Gopakumar-Gross form. For action
theories, these forms of the master field immediately give a number of new
free-algebraic packagings of the planar Schwinger-Dyson equations.Comment: 39 pages. Expanded historical remark
