Invariants in noncommutative dynamics
| Autor: | Alexandru Chirvasitu, Benjamin Passer |
|---|---|
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Conjecture 010102 general mathematics Mathematics - Operator Algebras 20G42 22C05 46L85 55S91 Hopf algebra 01 natural sciences Noncommutative geometry Iterated function Mathematics::Quantum Algebra Mathematics - Quantum Algebra 0103 physical sciences FOS: Mathematics Quantum Algebra (math.QA) Equivariant map 010307 mathematical physics Compact quantum group 0101 mathematics Invariant (mathematics) Abelian group Operator Algebras (math.OA) Analysis Mathematics |
| Zdroj: | Journal of Functional Analysis. 277:2664-2696 |
| ISSN: | 0022-1236 |
| Popis: | When a compact quantum group $H$ coacts freely on unital $C^*$-algebras $A$ and $B$, the existence of equivariant maps $A \to B$ may often be ruled out due to the incompatibility of some invariant. We examine the limitations of using invariants, both concretely and abstractly, to resolve the noncommutative Borsuk-Ulam conjectures of Baum-Dabrowski-Hajac. Among our results, we find that for certain finite-dimensional $H$, there can be no well-behaved invariant which solves the Type 1 conjecture for all free coactions of $H$. This claim is in stark contrast to the case when $H$ is finite-dimensional and abelian. In the same vein, it is possible for all iterated joins of $H$ to be cleft as comodules over the Hopf algebra associated to $H$. Finally, two commonly used invariants, the local-triviality dimension and the spectral count, may both change in a $\theta$-deformation procedure. Comment: 27 pages. To appear in Journal of Functional Analysis |
| Databáze: | OpenAIRE |
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