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We examine the algebraic structure of the matrix regularization for thewrapped membrane on $R^{10}\times S^1$ in the light-cone gauge. We give aconcrete representation for the algebra and obtain the matrix string theoryhaving the boundary conditions for the matrix variables corresponding to thewrapped membrane, which is referred to neither Seiberg and Sen's arguments norstring dualities. We also embed the configuration of the multi-wrapped membranein matrix string theory.Comment: 19 pages, 1 figure, references added, minor change

Wrapped membranes, matrix string theory and an infinite dimensional Lie algebra