Deformation methods in quantum groups

Anthony Giaquinto, University of Pennsylvania


The quantum matrix bialgebra M$\sb{q}$(2) and quantum plane k$\sbsp{q}{2}$ are constructed as preferred deformations of the classical matrix bialgebra and plane. The comultiplication for M$\sb{q}$(2) and the M$\sb{q}$(2)-coaction for k$\sbsp{q}{2}$ remain unchanged on all elements during the deformation. The construction of these quantum algebras is obtained by analyzing the invariant elements of certain representations of $S\sb{q}$(n), the quantum symmetric group, an infinite group having the usual symmetric group, S(n), as a quotient. The construction is possible for all values of the deformation parameter, q, except for roots of unity where certain constants necessary for the construction become infinite.

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Recommended Citation

Giaquinto, Anthony, "Deformation methods in quantum groups" (1991). Dissertations available from ProQuest. AAI9125649.