Quantum deformations for the diagonal R-matrices

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We consider two different types of deformations for the linear group $ GL(n)$ which correspond to using of a general diagonal R-matrix. Relations between braided and quantum deformed algebras and their coactions on a quantum plane are discussed. We show that tensor-grading-preserving differential calculi can be constructed on braided groups , quantum groups and quantum planes for the case of the diagonal R-matrix.
6 pages, Talk at Workshop on Supersymmetry and Quantum Groups, Dubna, 15-20 July 1993

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