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pro vyhledávání: '"Bischoff, Marcel"'
Autor:
Bischoff, Marcel, Karmakar, Pradyut
Let $L\subseteq \mathbb{R}^{n}$ an even lattice and $T_{L}=\mathbb{R}^{n}/L$ the associated torus. Associated with $L$ we construct $T_{L}$--kernel on a hyperfinite factor type $\mathcal{A}_{L}$, i.e. a monomorphism $T_{L}\to\mathsf{Out}(\mathcal{A}_
Externí odkaz:
http://arxiv.org/abs/2406.09667
Publikováno v:
Rev. Math. Phys. 35 (2023) 2350007
On a conformal net $\mathcal{A}$, one can consider collections of unital completely positive maps on each local algebra $\mathcal{A}(I)$, subject to natural compatibility, vacuum preserving and conformal covariance conditions. We call \emph{quantum o
Externí odkaz:
http://arxiv.org/abs/2204.14105
Publikováno v:
Ann. Henri Poincar\'e 23 (2022) 2979-3020
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity condition motivated by the study of inclusion of Quantum Fi
Externí odkaz:
http://arxiv.org/abs/2107.09345
We call a von Neumann algebra with finite dimensional center a multifactor. We introduce an invariant of bimodules over $\rm II_1$ multifactors that we call modular distortion, and use it to formulate two classification results. We first classify fin
Externí odkaz:
http://arxiv.org/abs/2010.01067
Publikováno v:
J. Funct. Anal. 281 (2021) 109004
Conformal inclusions of chiral conformal field theories, or more generally inclusions of quantum field theories, are described in the von Neumann algebraic setting by nets of subfactors, possibly with infinite Jones index if one takes non-rational th
Externí odkaz:
http://arxiv.org/abs/2007.12384
Autor:
Bischoff, Marcel, Jones, Corey
A $G$-graded extension of a fusion category $\mathcal{C}$ yields a categorical action of $G$ on the center $Z(\mathcal C)$. If the extension admits a spherical structure, we provide a method for recovering its fusion rules in terms of the action. We
Externí odkaz:
http://arxiv.org/abs/1909.02816
Autor:
Bischoff, Marcel
Using a result of Longo and Xu, we show that the anomaly arising from a cyclic permutation orbifold of order 3 of a holomorphic conformal net $\mathcal A$ with central charge $c=8k$ depends on the "gravitational anomaly" $k\pmod 3$. In particular, th
Externí odkaz:
http://arxiv.org/abs/1812.11910
Autor:
Bischoff, Marcel, Davydov, Alexei
Publikováno v:
Transformation Groups. 2020
We prove that commutative algebras in braided tensor categories do not admit faithful Hopf algebra actions unless they come from group actions. We also show that a group action allows us to see the algebra as the regular algebra in the representation
Externí odkaz:
http://arxiv.org/abs/1811.10528
In a physical system undergoing a continuous quantum phase transition, spontaneous symmetry breaking occurs when certain symmetries of the Hamiltonian fail to be preserved in the ground state. In the traditional Landau theory, a symmetry group can br
Externí odkaz:
http://arxiv.org/abs/1811.00434
Autor:
Bischoff, Marcel
Publikováno v:
Contemporary Mathematics 747, 115. 2020
We give a short proof for a well-known formula for the rank of a $G$-crossed braided extension of a modular tensor category.
Comment: 5 pages, v2 as sent for publications to Proceedings in Contemporary Mathematics series
Comment: 5 pages, v2 as sent for publications to Proceedings in Contemporary Mathematics series
Externí odkaz:
http://arxiv.org/abs/1807.06131