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“School of Physic”

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Paper   IPM / Physic / 6503
School of Physics
  Title:   A Simple Method for Constructing the Inhomogeneous Quantum Group IGLq(n) and Its Universal Enveloping Algebra UQ(igl(n))
1.  A. Shariati
2.  A. Aghamohammadi
  Status:   Published
  Journal: J. Math. Phys.
  No.:  27
  Vol.:  36
  Year:  1995
  Pages:   7103-7108
  Supported by:  IPM
We propse a simple and concise method to construct the inhomogeneous quantum group IGLq(n) and its universal enveloping algebra Uq(igl(n)). Our technique is based on embedding an n-dimensional quantum space in an n+1-dimensional one as the set xn+1=1. This is possible only if one considers the multiparametric quantum space whose parameters are fixed in a specific way. The quantum group IGLq(n) is then the subset of GLq(n+1), which leaves the xn+1=1 subset invariant. For the deformed universal enveloping algebra Uq(igl(n)), we will show that it can also be embedded in Uq(gl(n+1)), provided one uses the multiparametric deformation of U(gl(n+1)) with a specific choice of its parameters.

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