Über Borelunteralgebren von Quantengruppen

Diese Arbeit beschäftigt sich mit der Klassifikation aller Rechtscoidealunteralgebren C der Quantengruppen bei generischem q, mit der folgenden Eigenschaft: Alle endlichdimensionalen irreduziblen Darstellungen von C sind eindimensional und C ist maximal mit dieser Eigenschaft. Solche Rechtscoidealun...

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Bibliographic Details
Main Author: Vocke, Karolina
Contributors: Heckenberger, Istvan (Prof.) (Thesis advisor)
Format: Doctoral Thesis
Published: Philipps-Universität Marburg 2016
Online Access:PDF Full Text
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Table of Contents: This thesis contains steps towards the classification of all right coideal subalgebras C of a quantum group with generic q, where C has the additional property that all irreducible representations are 1-dimensional and C is maximal with this property. We call such a right coideal subalgebra a Borel subalgebra. First we construct for an arbitrary right coideal subalgebra a special choice of generators. Then we classify under some restrictions triangular Borelsubalgebras. We give a conjectural description of all Borel subalgebras in the general case, using the description of the graded algebra gr(C). Finally we work out explicitly all Borel subalgebras for Uq(sl2), Uq(sl3) without restrictions and all triangular Borel subalgebras for Uq(sl4).