37 papers
This paper proves that the star product for quantum symmetric pair coideal subalgebras is short, a result the authors use to provide new, elementary proofs of fundamental properties such as the existence of the bar involution and the intertwiner property of the quasi K-matrix without relying on the quasi K-matrix itself.
Inspired by the work of Enriquez and Furusho, this paper provides a stabilizer interpretation for both the linearized double shuffle Lie algebra and its extension accommodating multiple q-zeta values and multiple Eisenstein series, demonstrating that these stabilizers preserve the extension between the two algebras.
This paper generalizes the reflection theory of Nichols algebras to arbitrary coquasi-Hopf algebras with bijective antipode by establishing a braided monoidal equivalence that links finite-dimensional irreducible Yetter-Drinfeld modules admitting all reflections to semi-Cartan graphs, a framework applied to prove that a specific rank three example constitutes an affine Nichols algebra.
This paper develops pivotal and spherical versions of graded extension theory for tensor categories, defining corresponding Brauer-Picard 2-categorical groups, classifying extensions via monoidal 2-functors, and establishing an obstruction theory for extending these structures.
This paper constructs a braided balanced category of half-braided algebras and bimodules internal to a braided category to interpret stated skeins as a TQFT, specifically relating this construction to the Kerler-Lyubashenko TQFT in the case of finite-dimensional ribbon factorizable Hopf algebras.
This paper constructs analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of smooth oriented 4-manifolds by utilizing skein lasagna modules derived from equivariant and deformed link homology, while establishing non-vanishing results, decomposition theorems, and conditions for extending functoriality to immersed cobordisms.
This paper proposes and rigorously establishes a symmetrization relation between 4d BPS quivers and 3d symmetric quivers, demonstrating that the wall-crossing structure of 4d Argyres-Douglas theories is isomorphic to the unlinking of their 3d counterparts and that these symmetric quivers successfully capture the Schur indices of the original 4d theories.
This paper introduces the concept of strongly interlocked modules for vertex operator algebras to establish the well-definedness and key properties of graded pseudo-traces, subsequently applying this framework to fully characterize such modules for rank one Heisenberg and universal Virasoro algebras.
This paper introduces formal multiparameter quantum universal enveloping algebras (FoMpQUEA) as a generalization of Drinfeld's quantum groups, demonstrating that they are closed under toral twists and 2-cocycle deformations, establish a bijective correspondence with multiparameter Lie bialgebras via quantization and semiclassical limits, and prove that specialization and deformation processes commute.
This paper investigates the plane geometry of -rationals by constructing deformed Farey triangulations and modular surfaces, interpreting these numbers as Ford-like circles, and introducing Springborn operations as quadratic generalizations of Farey addition that correspond geometrically to the homothety centers of circle pairs.
This paper proves that the dual canonical bases of Drinfeld double quantum groups coincide with Berenstein–Greenstein's double canonical bases by utilizing the geometry of NKS quiver varieties to reinterpret their algebraic construction, thereby establishing their positivity and invariance under braid group actions.
This paper establishes that the degenerations of cohomological Hall algebras associated with 2-Calabi-Yau categories and preprojective algebras, with respect to the "less perverse" filtration, are isomorphic to the enveloping algebra of the current Lie algebra of the BPS Lie algebra, a result proven at the sheafified level and extended to torus-deformed settings to connect these structures with Maulik-Okounkov Yangians.
This paper constructs finite-dimensional quantum groups of type Super A at even roots of unity, classifies their ribbon structures to establish non-semisimple modular categories, and demonstrates that the resulting link invariants distinguish knots that are indistinguishable by the Jones or HOMFLYPT polynomials.
This paper establishes that finite non-invertible symmetries in 3+1d without topological line operators necessarily act invertibly on local operators, leading to a decomposition of general non-invertible symmetries into invertible actions and gauging interfaces, and deriving necessary conditions for such symmetries to be anomaly-free.
This paper establishes an explicit isomorphism between the equivariant nilpotent cohomological Hall algebra of one-dimensional sheaves on a surface resolving a Kleinian singularity and a completed positive half of the affine Yangian of the corresponding ADE Lie algebra, utilizing continuity theorems for -structures and multi-parameter Yangian definitions to characterize the algebra of cohomological Hecke operators.
This paper generalizes Carrollian Lie algebroids to the framework of -commutative (almost commutative) geometry via -Lie-Rinehart pairs, establishing foundational analogues for Carrollian structures and demonstrating their application through explicit constructions on the extended quantum plane and the noncommutative 2-torus.
This paper introduces a spectrally corrected polynomial approximation method for Quantum Singular Value Transformation that leverages prior knowledge of a subset of a matrix's eigenvalues to enforce exact interpolation at those points without increasing polynomial degree, thereby significantly reducing circuit depth while maintaining high fidelity and robustness.