One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry

Das, B. Krishna; Franz, Uwe; Kula, Anna; Skalski, Adam

doi:10.1007/s00209-015-1515-7

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Definition 22 a Triple (π1

Parametrization Of Generating Functionals1

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Cited by 6 publications

(3 citation statements)

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“…(5) for generating functionals on involutive Hopf algebras satisfying some symmetry condition, cf. [2]. Remark 2.6.…”

Section: Definition 22 a Triple (πmentioning

confidence: 96%

See 1 more Smart Citation

On the Lévy-Khinchin decomposition of generating functionals

Franz¹,

Gerhold²,

Thom³

2015

COSA

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“…(5) for generating functionals on involutive Hopf algebras satisfying some symmetry condition, cf. [2]. Remark 2.6.…”

Section: Definition 22 a Triple (πmentioning

confidence: 96%

“…(4) on the compact quantum groups SU q (N ) and U q (N ), cf [3],(5). for generating functionals on involutive Hopf algebras satisfying some symmetry condition, cf [2]…”

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confidence: 99%

On the Lévy-Khinchin decomposition of generating functionals

Franz¹,

Gerhold²,

Thom³

2015

COSA

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“…Not for nothing, did we explain in Remark 2.5 that we do not usually require that the cocycle be cyclic. (This can be done better under symmetry conditions on ψ; see Das, Franz, Kula, and Skalski [7]. )…”

Section: Parametrization Of Generating Functionalsmentioning

confidence: 99%

Hunt's Formula for $SU_q(N)$ and $U_q(N)$

Franz¹,

Kula²,

Lindsay³

et al. 2020

Preprint

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We provide a Hunt type formula for the infinitesimal generators of Lévy process on the quantum groups SU q (N ) and U q (N ). In particular, we obtain a decomposition of such generators into a gaussian part and a 'jump type' part determined by a linear functional that resembles the functional induced by the Lévy measure. The jump part on SU q (N ) decomposes further into parts that live on the quantum subgroups SU q (n), n ≤ N . Like in the classical Hunt formula for locally compact Lie groups, the ingredients become unique once a certain projection is chosen. There are analogous result for U q (N ).

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Around Property (T) for Quantum Groups

Daws¹,

Skalski

Viselter

2017

Commun. Math. Phys.

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Abstract:We study Property (T) for locally compact quantum groups, providing several new characterisations, especially related to operator algebraic ergodic theory. Quantum Property (T) is described in terms of the existence of various Kazhdan type pairs, and some earlier structural results of Kyed, Chen and Ng are strengthened and generalised. For second countable discrete unimodular quantum groups with low duals, Property (T) is shown to be equivalent to Property (T) 1,1 of Bekka and Valette. This is used to extend to this class of quantum groups classical theorems on 'typical' representations (due to Kerr and Pichot), and on connections of Property (T) with spectral gaps (due to Li and Ng) and with strong ergodicity of weakly mixing actions on a particular von Neumann algebra (due to Connes and Weiss). Finally, we discuss in the Appendix equivalent characterisations of the notion of a quantum group morphism with dense image.

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One-to-one correspondence between generating functionals and cocycles on quantum groups in presence of symmetry

Cited by 6 publications

References 17 publications

On the Lévy-Khinchin decomposition of generating functionals

On the Lévy-Khinchin decomposition of generating functionals

Hunt's Formula for $SU_q(N)$ and $U_q(N)$

Around Property (T) for Quantum Groups

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