Related papers: An approach to categorification of some small quan…
We categorify an idempotented form of quantum sl2 and some of its simple representations at a prime root of unity.
We categorify the Beilinson-Lusztig-MacPherson integral form of quantum sl(2) specialized at a prime root of unity.
We complete the classification of quantum subgroups of $SL_q(2)$ with $q$ a root of unity of arbitrary order, that is, Hopf algebra quotients of the quantum function algebras $\mathcal{O}_{q} (SL_2(\mathbb{C}))$.
We classify semisimple module categories over the tensor category of representations of quantum SL(2) extending previous results to the roots of unity and positive characteristic cases.
We start with the observation that the quantum group SL_q(2), described in terms of its algebra of functions has a quantum subgroup, which is just a usual Cartan group. Based on this observation we develop a general method of constructing…
We categorify the idempotented form of quantum sl(n).
We classify module categories over the category of representations of quantum $SL(2)$ in a case when $q$ is not a root of unity. In a case when $q$ is a root of unity we classify module categories over the semisimple subquotient of the same…
We categorify representations of quantum sl(n) whose highest weight is twice a fundamental weight.
We categorify the Casimir element of the idempotented form of quantum sl(2).
We categorify one-half of the quantum group associated to an arbitrary Cartan datum.
We give a geometric categorification of the Verma modules $M(\lambda)$ for quantum $\mathfrak{sl}_2$.
We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra gl(1|2).
In this article we construct a large family of $R$-matrices for various extensions of small quantum groups by grouplike elements. The extensions are in correspondence to lattices between root and weight lattice and admit $R$-matrices in…
In this note we give explicit isomorphisms of 2-categories between various versions of the categorified quantum group associated to a simply-laced Kac-Moody algebra. These isomorphisms are convenient when working with the categorified…
We describe a nonstandard version of the quantum plane, the one in the basis of divided powers at an even root of unity $q=e^{i\pi/p}$. It can be regarded as an extension of the "nearly commutative" algebra $C[X,Y]$ with $X Y =(-1)^p Y X$…
Let G be a connected, simply connected, simple complex algebraic group and let e be a primitive l-th root of 1, with l odd and 3 does not divide l if G is of type G_{2}. We determine all Hopf algebra quotients of the quantized coordinate…
We provide a combinatorial description of the monoidal category generated by the fundamental representation of the small quantum group of $\mathfrak{sl}_2$ at a root of unity $q$ of odd order. Our approach is diagrammatic, and it relies on…
We equip Ellis and Brundan's version of the odd categorified quantum group for sl(2) with a differential giving it the structure of a graded dg-2-supercategory. The presence of the super grading gives rise to two possible…
We define a family of the braid group representations via the action of the $R$-matrix (of the quasitriangular extension) of the restricted quantum $\mathfrak{sl}(2)$ on a tensor power of a simple projective module. This family is an…