Related papers: Categorification of quasi-split iquantum groups

In this paper we give an expository account of quasistrict symmetric monoidal 2-categories, as introduced by Schommer-Pries. We reformulate the definition using a graphical calculus called wire diagrams, which facilitates computations and…

We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…

In this note we give the quasi-isometry classification for a class of right angled Artin groups. In particular, we obtain the first such classification for a class of Artin groups with dimension larger than 2; our families exist in every…

We study finite quasi-quantum groups in their quiver setting developed recently by the first author in arXiv:0902.1620 and arXiv:0903.1472. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation…

We present a comprehensive generalization of Lusztig's braid group symmetries for quasi-split iquantum groups. Specifically, we give 3 explicit rank one formulas for symmetries acting on integrable modules over a quasi-split iquantum group…

We introduce a series of $\Z_2^n$-graded quasialgebras $\bbP_n(m)$ which generalizes Clifford algebras, higher octonions, and higher Cayley algebras. The constructed series of algebras and their minor perturbations are applied to contribute…

This survey covers some of the results contained in the papers by Costantino, Geer and Patureau (https://arxiv.org/abs/1202.3553) and by Blanchet, Costantino, Geer and Patureau (https://arxiv.org/abs/1404.7289). In the first one the authors…

The class of all quasigroups is covered by six classes: the class of all asymmetric quasigroups and five varieties of quasigroups (commutative, left symmetric, right symmetric, semi-symmetric and totally symmetric). Each of these classes is…

A geometric realization of the quasi-split affine iquantum group of type $\mathrm{AIII}_{2n-1}^{(\tau)}$ was given by Wang and the second author, in terms of equivariant K-groups of Steinberg varieties of type C. As a completion of that…

We construct knot invariants categorifying the quantum knot variants for all representations of quantum groups. We show that these invariants coincide with previous invariants defined by Khovanov for sl_2 and sl_3 and by Mazorchuk-Stroppel…

We provide a classification of finite-dimensional graded pointed Majid algebras generated by finite abelian groups as group-like elements and a set of quasi-commutative skew-primitive elements. This amounts to a classification of finite…

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An…

The first example of a quantum group was introduced by P.~Kulish and N.~Reshetikhin. In their paper "Quantum linear problem for the sine-Gordon equation and higher representations" published in Zap. Nauchn. Sem. LOMI, 1981, Volume 101…

This paper determines almost symmetric numerical semigroups with maximal reduced type completely. In addition, this paper classifies MED-semigroups with maximal reduced type.

We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants defined in arXiv:1008.3103 and arXiv:0910.1624, respectively. In this…

We introduce semisimple 2-categories, fusion 2-categories, and spherical fusion 2-categories. For each spherical fusion 2-category, we construct a state-sum invariant of oriented singular piecewise-linear 4-manifolds.

In this paper we categorify the q-Schur algebra S(n,d) as a quotient of Khovanov and Lauda's diagrammatic 2-category U(sln). We also show that our 2-category contains Soergel's monoidal category of bimodules of type A, which categorifies…

In Part I of this series we presented the general ideas of applying group-algebraic methods for describing quantum systems. The treatment was there very "ascetic" in that only the structure of a locally compact topological group was used.…

We define a notion of groupoidal 2-quasi-categories and show that they are the fibrant objects of a model structure on the category of $\Theta_2$-sets. We show that this model category is Quillen equivalent to the Kan-Quillen model category…

Starting from the groupoid approach to Schwinger's picture of Quantum Mechanics, a proposal for the description of symmetries in this framework is advanced.It is shown that, given a groupoid $G\rightrightarrows \Omega$ associated with a…