Abstract
In the development of the activity started on lattice analogues of W algebras, we define the notion of a lattice W ∞ algebra, associated with a lattice integrable system with an infinite set of fields. Various kinds of reduction to lattice W N algebras, related to discrete N-KdV hierarchies are described. We also discuss the connection of our results with those obtained in the papers of Xiong [Phys. Lett. B 279 (1992) 347] and Bonora [Multimatrix models without continuous limit, preprint SISSA-ISAS 211/92/EP(1992)].
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