Related papers: Trace decategorification of categorified quantum s…

We define the universal sl3-link homology, which depends on 3 parameters, following Khovanov's approach with foams. We show that this 3-parameter link homology, when taken with complex coefficients, can be divided into 3 isomorphism…

We categorify an idempotented form of quantum sl2 and some of its simple representations at a prime root of unity.

We categorify a quantized Heisenberg algebra associated to a finite subgroup of SL(2,C).

Using a modified foam evaluation, we give a categorification of the Alexander polynomial of a knot. We also give a purely algebraic version of this knot homology which makes it appear as the infinite page of a spectral sequence starting at…

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In this paper we construct explicitly such…

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…

The purpose of this paper is to study categorifications of tensor products of finite dimensional modules for the quantum group for sl(2). The main categorification is obtained using certain Harish-Chandra bimodules for the complex Lie…

We prove that the equivariant derived category for a finite subgroup of GL(3,C) has a semi-orthogonal decomposition into the derived category of a certain partial resolution, called a maximal Q-factorial terminalization, of the…

We combine previous work on coalgebraic logic with the coalgebraic traces semantics of Hasuo, Jacobs, and Sokolova.

We construct quantum invariants of 3-manifolds based on a $\mathfrak{sl}_3$ matrix dilogarithm proposed by Kashaev. This matrix dilogarithm is an $\mathfrak{sl}_3$ analogue of the (cyclic) quantum dilogarithm used to define Kashaev's…

Lieb and Solovej \cite{liebsolBloch} studied traces of quantum channels, defined by the leading component in the decomposition of the tensor product of two irreducible representations of $SU(2)$, to establish a Wehrl-type inequality for…

The q-field theories are constructed by substituting quantum groups for the usual Lie groups. In earlier papers this construction was carried out for the quantum group SU_q(2). Here the investigation is extended to SL_q(3). The resulting…

By introducing a notion of smooth connection for unbounded $KK$-cycles, we show that the Kasparov product of such cycles can be defined directly, by an algebraic formula. In order to achieve this it is necessary to develop a framework of…

Using the isomorphism $\mathfrak{o}(3;\mathbb{C})\simeq\mathfrak{sl}(2;\mathbb{C})$ we develop a new simple algebraic technique for complete classification of quantum deformations (the classical $r$-matrices) for real forms…

In their paper entitled "Quantum Enhancements and Biquandle Brackets," Nelson, Orrison, and Rivera introduced biquandle brackets, which are customized skein invariants for biquandle-colored links. These invariants generalize the Jones…

A new class of algebras have been introduced by Khovanov and Lauda and independently by Rouquier. These algebras categorify one-half of the Quantum group associated to arbitrary Cartan data. In this paper, we use the combinatorics of Lyndon…

We study the only missing case in the classification of quantum SL(3,C)'s undertaken in our paper [J. of Algebra 213 (1999), 721--756; see http://arxiv.org/abs/q-alg/9711005], thereby completing this classification.

We introduce a large class of bicovariant differential calculi on any quantum group $A$, associated to $Ad$-invariant elements. For example, the deformed trace element on $SL_q(2)$ recovers Woronowicz' $4D_\pm$ calculus. More generally, we…

The combined trace (i.e., comtrace) notion was introduced by Janicki and Koutny in 1995 as a generalization of the Mazurkiewicz trace notion. Comtraces are congruence classes of step sequences, where the congruence relation is defined from…

We introduce the concept of tied links in the solid torus, which generalize naturally the concept of tied links in $S^3$ previously introduced by Aicardi and Juyumaya. We also define an invariant of these tied links by using skein…