Deformation methods in quantum groups
Abstract
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.
Subject Area
Mathematics
Recommended Citation
Giaquinto, Anthony, "Deformation methods in quantum groups" (1991). Dissertations available from ProQuest. AAI9125649.
https://repository.upenn.edu/dissertations/AAI9125649