The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
205, American Mathematical Society, Providence, RI, 2015
8 Pith papers cite this work. Polarity classification is still indexing.
8
Pith papers citing it
citation-role summary
background 1
citation-polarity summary
roles
background 1polarities
background 1representative citing papers
Develops an operator-algebraic framework for fusion category symmetries on (1+1)D lattices, proving realization conditions via integer dimensions and fiber functors plus anomaly-enforced gaplessness theorems.
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
Proper outerness is automatic for finite index outer endomorphisms of simple C*-algebras, implying automatic freeness for outer actions of unitary tensor categories.
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
citing papers explorer
-
The disoriented skein and iquantum Brauer categories
The disoriented skein category is defined and shown equivalent to the iquantum Brauer category, serving as an interpolating module category with full incarnation functors to modules over iquantum enveloping algebras.
-
An operator algebraic approach to fusion category symmetry on the lattice
Develops an operator-algebraic framework for fusion category symmetries on (1+1)D lattices, proving realization conditions via integer dimensions and fiber functors plus anomaly-enforced gaplessness theorems.
-
Lattice Models for Phases and Transitions with Non-Invertible Symmetries
A method is given to construct UV anyonic chain lattice models from SymTFT data realizing IR phases and transitions with non-invertible symmetries, illustrated with Rep(S3).
-
Universal fusion category symmetries on tensor products of infinite-dimensional Hilbert spaces
Any unitary fusion category can be realized as symmetries on tensor products of infinite-dimensional Hilbert spaces via stabilized anyon chains, with equivalence between different chains of the same category.
-
Properly Outer Actions of Tensor Categories on C$^*$-algebras
Proper outerness is automatic for finite index outer endomorphisms of simple C*-algebras, implying automatic freeness for outer actions of unitary tensor categories.
-
On Hecke and asymptotic categories for a family of complex reflection groups
Constructs Hecke algebras and asymptotic versions for G(M,M,N) complex reflection groups by generalizing the dihedral case.
-
Topological symmetry in quantum field theory
Authors introduce a TFT-based framework for finite topological symmetries in QFT, including gauging, condensation defects, and duality defects, with an appendix on finite homotopy theories.
-
ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.