37 papers
This paper establishes a geometric group theory framework for right quasigroups by introducing graph markings and invariants to characterize their Cayley (di)graphs, thereby proving that all racks are realizable by their full Cayley graphs and providing graph-theoretic characterizations for various algebraic structures.
This paper extends support variety theory from the compact to the non-compact part of a monoidal triangulated category in the noncommutative setting, establishing conditions under which the extended theory detects the zero object and thereby confirming a portion of a conjecture by the second author, Nakano, and Yakimov regarding central cohomological support in stable categories of finite tensor categories.
This paper provides explicit formulas for the coproducts of modified Drinfeld-Cartan generating series for the Yangian in type and the quantum affine algebra in type , while also presenting an explicit construction of positive prefundamental representations for the latter.
This paper systematically characterizes categorical duality operators on spin and anyon chains with internal fusion category symmetry by parameterizing them via quantum cellular automata and associated bimodule categories, demonstrating that such operators form a simplex whose extreme points correspond to simple objects, and proving that these structures inevitably flow to weakly integral fusion categories in the infrared limit when defined on tensor product Hilbert spaces.
This paper constructs modular families of quantum-integrable elliptic long-range spin chains with q-deformed interactions by freezing spin-Ruijsenaars systems at classical equilibrium configurations, thereby providing a unified framework that interpolates between nearest-neighbour and long-range models while encompassing various known integrable chains and their deformations.
This paper constructs a monoidal category of representations for the quantum affine algebra of a simple, simply connected, simply laced algebraic group, whose Grothendieck ring contains a cluster algebra with an initial seed corresponding to the coordinate ring of twisted products of flag varieties, including braid varieties and reduced double Bruhat cells.
This paper establishes a cubic braid-type skein theory for the Links-Gould polynomial, proving its universal computability for oriented links and demonstrating its equivalence to the -polynomial, thereby unifying their shared properties such as specialization to the Alexander polynomial and providing a Seifert genus bound.
This paper introduces a Fourier-type formalism on non-commutative spaces to establish two versions of the Hörmander-Mikhlin -multiplier theorem for locally compact Kac groups and semi-finite von Neumann algebras, which generalize classical results and are applied to evolution equations in non-commutative settings.
This paper establishes that the -deformed modular group specializes to a finite group at a complex parameter if and only if is a primitive -th root of unity for , in which cases the resulting groups are isomorphic to specific binary polyhedral groups, while the case yields an infinite but "mild" structure with applications to Jones polynomials.
This paper establishes a natural -multicategory structure on moduli spaces of pseudo-holomorphic polygons to provide a uniform operadic framework for various -type structures, including Fukaya categories, as algebras over differential graded -multicategories.
This paper investigates the representation theory of shifted super Yangians and finite -superalgebras of type A by establishing a criterion for the finite dimensionality of irreducible modules, deriving an explicit Gelfand-Tsetlin character formula for Verma modules, and proving that the centers of these algebras associated with even nilpotent elements are isomorphic to the center of the universal enveloping superalgebra.
This paper introduces shifted quantum affine symmetric pairs of split simply-laced type and constructs their GKLO representations, providing a complete proof that the proposed formulas define a valid representation.
This paper establishes a Murnaghan-Nakayama rule for the irreducible characters of the cyclotomic Hecke algebra on Shoji's standard elements, providing a direct combinatorial method to compute full character tables, deriving dual iterative formulas, and applying these results to obtain new character sum formulas and orthogonality relations.
This paper provides a proof of Lusztig's conjectural multiplicity formula for non-restricted modules over the De Concini-Kac type quantized enveloping algebra at an odd prime power root of unity.
This paper explicitly computes the spectral metric, torsion, and Einstein tensors for a specific nontrivial spectral triple on a noncommutative torus, demonstrating that both the torsion and the Einstein tensor identically vanish.
This paper establishes an isomorphism between the classical quasi-shuffle and the recently defined shuffle Hopf algebras for multiple zeta values by utilizing quasi-symmetric functions, while comparing this result to the well-known isomorphism by Hoffman, Newman, and Radford.
This paper establishes a non-unitary version of the Bisognano-Wichmann property and proves Haag duality for nets of smeared Wightman fields by deriving Tomita-Takesaki-like results directly from Wightman axioms, thereby extending these fundamental algebraic quantum field theory concepts to non-unitary theories where traditional Hilbert space functional analysis tools are unavailable.
This paper investigates the local-triviality dimensions of actions on -algebras within noncommutative Borsuk-Ulam theory, demonstrating that free actions do not necessarily possess finite weak local-triviality dimensions and that these invariants can exhibit discontinuity or exceed fiber values in continuous fields, while establishing conditions for upper semicontinuity through examples involving noncommutative tori and spheres.
This paper establishes that the symmetric algebra of the Bergman space on the unit disk forms a natural algebra over a square-integrable suboperad of holomorphic disk embeddings, which is identified with the affine Heisenberg vertex operator algebra and used to construct metric-dependent invariants for two-dimensional Riemannian manifolds via conformally flat factorization homology.
This paper investigates finiteness conditions on skew braces, specifically -skew braces with additive groups, by establishing structural analogs to finite conjugacy and demonstrating how these properties characterize infinite set-theoretic solutions of the Yang-Baxter equation that behave similarly to finite ones.