Zobrazeno 1 - 10
of 179
pro vyhledávání: '"Soltan, P. M."'
Autor:
Paupa, Wojciech, Sołtan, Piotr M.
We compute the independence number, zero-error capacity, and the values of the Lov\'asz function and the quantum Lov\'asz function for the quantum graph associated to the partial trace quantum channel $\operatorname{Tr}_n\otimes\mathrm{id}_k\colon\op
Externí odkaz:
http://arxiv.org/abs/2408.16858
Autor:
Krajczok, Jacek, Sołtan, Piotr M.
We introduce and study a number of invariants of locally compact quantum groups defined by their scaling and modular groups and the spectrum of their modular elements. Focusing mainly on compact quantum groups we consider the question whether trivial
Externí odkaz:
http://arxiv.org/abs/2311.01204
Autor:
Krajczok, Jacek, Sołtan, Piotr M.
For each $\lambda\in\left]0,1\right]$ we exhibit an uncountable family of compact quantum groups $\mathbb{G}$ such that the von Neumann algebra $\mathsf{L}^{\!\infty}(\mathbb{G})$ is the injective factor of type $\mathrm{III}_\lambda$ with separable
Externí odkaz:
http://arxiv.org/abs/2203.10976
For given quantum (non-commutative) spaces $\mathbb{P}$ and $\mathbb{O}$ we study the quantum space of maps $\mathbb{M}_{\mathbb{P},\mathbb{O}}$ from $\mathbb{P}$ to $\mathbb{O}$. In case of finite quantum spaces these objects turn out to be behind a
Externí odkaz:
http://arxiv.org/abs/2105.07820
We prove a number of results having to do with equipping type-I $\mathrm{C}^*$-algebras with compact quantum group structures, the two main ones being that such a compact quantum group is necessarily co-amenable, and that if the $\mathrm{C}^*$-algebr
Externí odkaz:
http://arxiv.org/abs/2008.03772
Autor:
Krajczok, Jacek, Sołtan, Piotr M.
We show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz C*-algebra does not admit any compact quantum group structure. We prove that if such a structure existed the resulting compact quantum group would simultaneously be o
Externí odkaz:
http://arxiv.org/abs/2005.02967
Akademický článek
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Akademický článek
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Autor:
Sołtan, Piotr M.
Starting with the braided quantum group $\operatorname{SU}_q(2)$ for a complex deformation parameter $q$ we perform the construction of the quotient $\operatorname{SU}_q(2)/\mathbb{T}$ which serves as a model of a quantum sphere. Then we follow the r
Externí odkaz:
http://arxiv.org/abs/1909.05000
Idempotent states on locally compact quantum semigroups with weak cancellation properties are shown to be Haar states on a certain sub-object described by an operator system with comultiplication. We also give a characterization of the situation when
Externí odkaz:
http://arxiv.org/abs/1905.11726