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Unipotent Radicals of the Standard Borel and Parabolic Subgroups in Quantum Special Linear Groups


In this dissertation we find noncommutative analogues of the coordinate rings of the unipotent radicals of the standard Borel and standard parabolic subgroups in quantum special linear groups. In each case, two subalgebras are defined, both of which can be considered quantizations of the unipotent radical of a standard Borel or a standard parabolic subgroup. Presentations are given for these algebras. It is also shown that these algebras arise as a coinvariant subalgebra of a natural comodule algebra action induced from the Hopf algebra structure on quantum special linear groups.

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