26 citations · 180 across the 37 of their papers we have counts for
16 papers · 1 filter
Modified trace is a symmetrised integral
Anna Beliakova, Christian Blanchet, Azat M. Gainutdinov
A modified trace for a finite k-linear pivotal category is a family of linear forms on endomorphism spaces of projective objects which has cyclicity and so-called partial trace pro…
Cyclicity for categorified quantum groups
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
We equip the categorified quantum group attached to a KLR algebra and an arbitrary choice of scalars with duality functor which is cyclic, that is, such that f=f^** for all 2-morph…
Current algebras and categorified quantum groups
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
We identify the trace, or 0th Hochschild homology, of type ADE categorified quantum groups with the corresponding current algebra of the same type. To prove this, we show that 2-re…
Trace as an alternative decategorification functor
Anna Beliakova, Zaur Guliyev, Kazuo Habiro +1
Categorification is a process of lifting structures to a higher categorical level. The original structure can then be recovered by means of the so-called "decategorification" funct…
Trace decategorification of categorified quantum sl(3)
Marko Živković
We prove that the trace of categorified quantum sl(3) introduced by M. Khovanov and A. Lauda can also be identified with quantum sl(3), thus providing an alternative way of decateg…
Trace decategorification of categorified quantum sl(2)
Anna Beliakova, Kazuo Habiro, Aaron D. Lauda +1
The trace or the th Hochschild--Mitchell homology of a linear category may be regarded as a kind of decategorification of . We compute traces of the t…
A categorification of the ribbon element in quantum sl(2)
Anna Beliakova, Kazuo Habiro
We define a bicomplex whose Euler characteristic is the idempotented version of the ribbon element of quantum sl(2). We show that properties of this bicomplex descend to the centra…
Steenrod Structures on Categorified Quantum Groups
Anna Beliakova, Benjamin Cooper
Categorified quantum groups play an increasing role in quantum topology and representation theory. The Steenrod algebra is a fundamental component of algebraic topology. In this pa…
Categorified quantum sl(2) is an inverse limit of flag 2-categories
Anna Beliakova, Aaron D. Lauda
We prove that categorified quantum sl(2) is an inverse limit of Flag 2-categories defined using cohomology rings of iterated flag varieties. This inverse limit is an instance of a…
On the integrality of Witten-Reshetikhin-Turaev 3-manifold invariants
Anna Beliakova, Qi Chen, Thang Le
We prove that the SU(2) and SO(3) Witten-Reshetikhin-Turaev invariants of any 3-manifold with any colored link inside at any root of unity are algebraic integers.
A categorification of the Casimir of quantum sl(2)
Anna Beliakova, Mikhail Khovanov, Aaron D. Lauda
We categorify the Casimir element of the idempotented form of quantum sl(2).
Unified quantum invariants and their refinements for homology 3-spheres with 2-torsion
Anna Beliakova, Christian Blanchet, Thang T. Q. Le
For every rational homology 3-sphere with 2-torsion only we construct a unified invariant (which takes values in a certain cyclotomic completion of a polynomial ring), such that th…
Categorification of the colored Jones polynomial and Rasmussen invariant of links
Anna Beliakova, Stephan Wehrli
We define a family of formal Khovanov brackets of a colored link depending on two parameters. The isomorphism classes of these brackets are invariants of framed colored links. The…
Laplace transform and universal sl(2) invariants
Anna Beliakova, Christian Blanchet, Thang Le
We develop a Laplace transform method for constructing universal invariants of 3-manifolds. As an application, we recover Habiro's theory of integer homology 3-spheres and extend i…
Geometric construction of spinors in orthogonal modular categories
Anna Beliakova
A geometric construction of Z_2-graded orthogonal modular categories is given. Their 0-graded parts coincide with categories previously obtained by Blanchet and the author from the…
Skein construction of idempotents in Birman-Murakami-Wenzl algebras
Anna Beliakova, Christian Blanchet
We give skein theoretic formulas for minimal idempotents in the Birman-Murakami-Wenzl algebras. These formulas are then applied to derive various known results needed in the constr…