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| Paper IPM / P / 6503 |
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| Abstract: | |||||
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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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