Results 31 to 40 of about 5,500 (151)
PARITY, SKEIN POLYNOMIALS AND CATEGORIFICATION [PDF]
Journal of Knot Theory and Its Ramifications, 2012 We investigate an application of crossing parity for the bracket expansion of the Jones polynomial for virtual knots. In addition we consider an application of parity for the arrow polynomial as well as for the categorifications of both polynomials. We present a number of examples found through our calculations.
Kaestner, Aaron M., Kauffman, Louis H.
openaire +2 more sources
Diagrammatics for Soergel Categories
International Journal of Mathematics and Mathematical Sciences, 2010 The monoidal category of Soergel bimodules can be thought of as a categorification of the Hecke algebra of a finite Weyl group. We present this category, when the Weyl group is the symmetric group, in the language of planar diagrams with local generators
Ben Elias, Mikhail Khovanov
doaj +1 more source
Dominance order and monoidal categorification of cluster algebras
, 2019 We study a compatibility relationship between Qin's dominance order on a cluster algebra $\mathcal{A}$ and partial orderings arising from classifications of simple objects in a monoidal categorification $\mathcal{C}$ of $\mathcal{A}$.
Casbi, Elie
core +3 more sources
, 1998 51 pages LaTeX with 9 encapsulated Postscript ...
Baez, John C., Dolan, James
openaire +2 more sources
CATEGORIFICATION OF THE DICHROMATIC POLYNOMIAL FOR GRAPHS [PDF]
Journal of Knot Theory and Its Ramifications, 2008 For each graph and each positive integer n, we define a chain complex whose graded Euler characteristic is equal to an appropriate n-specialization of the dichromatic polynomial. This also gives a categorification of n-specializations of the Tutte polynomial of graphs.
openaire +2 more sources
Categorification of Highest Weight Modules via Khovanov-Lauda-Rouquier Algebras
, 2012 In this paper, we prove Khovanov-Lauda's cyclotomic categorification conjecture for all symmetrizable Kac-Moody algebras. Let $U_q(g)$ be the quantum group associated with a symmetrizable Cartan datum and let $V(\Lambda)$ be the irreducible highest ...
G. Lusztig +12 more
core +1 more source
On matrix-model approach to simplified Khovanov–Rozansky calculus
Physics Letters B, 2015 Wilson-loop averages in Chern–Simons theory (HOMFLY polynomials) can be evaluated in different ways – the most difficult, but most interesting of them is the hypercube calculus, the only one applicable to virtual knots and used also for categorification (
A. Morozov, And. Morozov, A. Popolitov
doaj +1 more source
Categorification of quantum symmetric pairs I [PDF]
, 2018 We categorify a coideal subalgebra of the quantum group of $\mathfrak{sl}_{2r+1}$ by introducing a $2$-category \`a la Khovanov-Lauda-Rouquier, and show that self-dual indecomposable $1$-morphisms categorify the canonical basis of this algebra.
Bao, H., Shan, P., Wang, W., Webster, B.
core +2 more sources
GL‐algebras in positive characteristic II: The polynomial ring
Proceedings of the London Mathematical Society, Volume 131, Issue 6, December 2025.Abstract We study GL$\mathbf {GL}$‐equivariant modules over the infinite variable polynomial ring S=k[x1,x2,…,xn,…]$S = k[x_1, x_2, \ldots, x_n, \ldots]$ with k$k$ an infinite field of characteristic p>0$p > 0$. We extend many of Sam–Snowden's far‐reaching results from characteristic zero to this setting.
Karthik Ganapathy
wiley +1 more source
A Note on the Categorification of Lie Algebras [PDF]
, 2013 In this short note we study Lie algebras in the framework of symmetric monoidal categories. After a brief review of the existing work in this field and a presentation of earlier studied and new examples, we examine which functors preserve the structure of a Lie algebra.
Vercruysse, Joost, Goyvaerts, Isar
openaire +4 more sources