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Fundamental isomorphism theorems for quantum groups

2017

The lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the group into "chunks" (subquotients) that can then be compared to one another in various ways. Examples of results in this class would be the Noether isomorphism theorems, Zassenhaus' butterfly lemma, the Schreier refinement theorem for subnormal series of subgroups, the Dedekind modularity law, and last but not least the Jordan-H\"older theorem. We discuss analogues of the above-mentioned results in the context of locally compact quantum groups and linearly reductive quantum groups. The nature of the two cases is different: the former is operator algebraic and the latt…

General MathematicsGroup Theory (math.GR)01 natural sciences0103 physical sciencesMathematics - Quantum AlgebraQuantum no-deleting theoremFOS: MathematicsQuantum Algebra (math.QA)Compact quantum groupLocally compact space0101 mathematicsOperator Algebras (math.OA)MathematicsZassenhaus lemmaLocally compact quantum group010102 general mathematicsMathematics - Operator AlgebrasFunctional Analysis (math.FA)AlgebraMathematics - Functional Analysis46L89 46L85 46L52 16T20 20G42Isomorphism theoremQuantum algorithmSchreier refinement theorem010307 mathematical physicsMathematics - Group Theory
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