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.