  In this paper we define infinite-dimensional algebra and its representation,
whose basis is naturally identified with semi-infinite configurations of the
square ladder model. We also extrapolate the ideas for the cyclic 3-leg
triangular ladder model. All of these propose a way for generalization, which
leads to representations of N = 2, ... algebras.
  Keywords: 2D lattice, square ladder, triangular ladder, conformal algebra,
semi-infinite forms, fermions, quadratic algebra, superfrustration, graded
Euler characteristic, cohomology, deformation, Jacobi triple product,
superalgebras, operator algebras, N = 2, ... algebras.
