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We construct the parabosonic string formalism based on the paraquantizationof both the center of mass variables and the excitation modes of the string. Acritical study of the different commutators of the Poincar\'{e} algebra basedon the redefinition of its generators and the direct treatment using trilinearrelations is done. Space-time critical dimensions $D$ as functions of theparaquantization order $Q$ are obtained.Comment: Latex,16 pages; v2 : published version, with numbering of formulas  and conclusion correcte

Poincare algebra and space-time critical dimensions for parabosonic strings