New loop equations for all genera in c=21 non-critical string
theory are constructed. Our loop equations include two types of loops, loops
with all Ising spins up (+ loops) and those with all spins down ( − loops).
The loop equations generate an algebra which is a certain extension of W3
algebra and are equivalent to the W3 constraints derived before in the
matrix-model formulation of 2d gravity. Application of these loop equations to
construction of Hamiltonian for c=21 string field theory is
considered.Comment: 21 pages, LaTex file, no figure