منابع مشابه
Categorification and Groupoidification of the Heisenberg Algebra
These lectures, prepared for Higher Structures in China III, held in Changchun, Aug 2012, describe a relationship between two forms of categorification of algebras by giving a combinatorial model for Khovanov’s categorification of the Heisenberg algebra in a 2-category of spans of groupoids. This is joint work with Jamie Vicary. The goal here is to describe two notions of “categorifying an alge...
متن کاملA Survey of Heisenberg Categorification via Graphical Calculus
In this expository paper we present an overview of various graphical categorifications of the Heisenberg algebra and its Fock space representation. We begin with a discussion of “weak” categorifications via modules for Hecke algebras and “geometrizations” in terms of the cohomology of the Hilbert scheme of points on the resolution of a simple singularity. We then turn our attention to more rece...
متن کاملCategorification and Heisenberg doubles arising from towers of algebras
The Grothendieck groups of the categories of finitely generated modules and finitely generated projective modules over a tower of algebras can be endowed with (co)algebra structures that, in many cases of interest, give rise to a dual pair of Hopf algebras. Moreover, given a dual pair of Hopf algebras, one can construct an algebra called the Heisenberg double, which is a generalization of the c...
متن کاملOn Categorification
We review several known categorification procedures, and introduce a functorial categorification of group extensions with applications to non-abelian group cohomology. Categorification of acyclic models and of topological spaces are briefly mentioned.
متن کاملLink homology and categorification
This is a short survey of algebro-combinatorial link homology theories which have the Jones polynomial and other link polynomials as their Euler characteristics. 2000 Mathematics Subject Classification: 57M25, 57Q45.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Algebraic Combinatorics
سال: 2019
ISSN: 2589-5486
DOI: 10.5802/alco.73