On the $${\ell }^2$$ℓ2-Betti numbers of universal quantum groups
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DOI: 10.1007/s00208-017-1531-5
Abstract: We show that the first $${\ell }^2$$ℓ2-Betti number of the duals of the free unitary quantum groups is one, and that all $${\ell }^2$$ℓ2-Betti numbers vanish for the duals of the quantum automorphism groups of… read more here.
Keywords: ell betti; universal quantum; quantum groups; numbers universal ... See more keywords
Classification of Quantum Groups via Galois Cohomology
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DOI: 10.1007/s00220-019-03597-z
Abstract: The first example of a quantum group was introduced by P. Kulish and N. Reshetikhin. In the paper Kulish et al. (J Soviet Math 23:2435–2441, 1983), they found a new algebra which was later called $$U_q (\mathfrak {sl}(2))$$… read more here.
Keywords: quantum; quantum groups; galois cohomology; cohomology ... See more keywords
A Family of New Borel Subalgebras of Quantum Groups
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DOI: 10.1007/s10468-020-09956-y
Abstract: We construct a family of right coideal subalgebras of quantum groups, which have the property that all irreducible representations are one-dimensional, and which are maximal with this property. The obvious examples for this are the… read more here.
Keywords: borel subalgebras; family new; quantum groups; subalgebras quantum ... See more keywords
Inductive limits of compact quantum groups and their unitary representations
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DOI: 10.1007/s11005-021-01468-0
Abstract: We will introduce the notion of inductive limits of compact quantum groups as $W^*$-bialgebras equipped with some additional structures. We also formulate their unitary representation theories. Those give a more explicit representation-theoretic meaning to our… read more here.
Keywords: inductive limits; unitary representations; quantum groups; compact quantum ... See more keywords
Representations of quantum groups at roots of unity, Whittaker vectors and q-W algebras
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DOI: 10.1016/j.jalgebra.2018.06.007
Abstract: Abstract Let U e ( g ) be the standard simply connected version of the Drinfeld–Jumbo quantum group at an odd m-th root of unity e. The center of U e ( g ) contains… read more here.
Keywords: whittaker vectors; quantum groups; representations quantum; roots unity ... See more keywords
Entropic uncertainty relations under localizations on discrete quantum groups
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DOI: 10.1063/1.5037820
Abstract: The uncertainty principle has been established within the framework of locally compact quantum groups in recent years. This paper demonstrates that entropic uncertainty relations can be strengthened under localizations on discrete quantum groups, which is… read more here.
Keywords: quantum; entropic uncertainty; uncertainty relations; localizations discrete ... See more keywords
Lévy–Khintchine decompositions for generating functionals on algebras associated to universal compact quantum groups
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DOI: 10.1142/s0219025718500170
Abstract: We study the first and second cohomology groups of the ∗-algebras of the universal unitary and orthogonal quantum groups UF+ and OF+. This provides valuable information for constructing and classifying Levy processes on these quantum… read more here.
Keywords: quantum; decompositions generating; quantum groups; khintchine decompositions ... See more keywords
Trace of powers of representations of finite quantum groups
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DOI: 10.1142/s0219498820501248
Abstract: In this paper, we study (asymptotic) properties of the ∗-distribution of irreducible characters of finite quantum groups. We proceed in two steps, first examining the representation theory to determine irreducible representations and their powers, then… read more here.
Keywords: trace powers; distribution; quantum groups; powers representations ... See more keywords
Ergodic Actions of Compact Quantum Groups from Solutions of the Conjugate Equations
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DOI: 10.1215/21562261-2017-0005
Abstract: AbstractWe use a tensor C ∗ –category with conjugates and two quasitensor func-tors into the category of Hilbert spaces to define a C ∗ –algebra dependingfunctorially on this data. A particular case of this construction… read more here.
Keywords: conjugate equations; ergodic actions; actions compact; quantum groups ... See more keywords