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A general approach to Heisenberg categorification via wreath product algebras
- Publication Year :
- 2015
- Publisher :
- arXiv, 2015.
-
Abstract
- We associate a monoidal category $\mathcal{H}_B$, defined in terms of planar diagrams, to any graded Frobenius superalgebra $B$. This category acts naturally on modules over the wreath product algebras associated to $B$. To $B$ we also associate a (quantum) lattice Heisenberg algebra $\mathfrak{h}_B$. We show that, provided $B$ is not concentrated in degree zero, the Grothendieck group of $\mathcal{H}_B$ is isomorphic, as an algebra, to $\mathfrak{h}_B$. For specific choices of Frobenius algebra $B$, we recover existing results, including those of Khovanov and Cautis--Licata. We also prove that certain morphism spaces in the category $\mathcal{H}_B$ contain generalizations of the degenerate affine Hecke algebra. Specializing $B$, this proves an open conjecture of Cautis--Licata.<br />Comment: 46 pages. v2: Several sign errors and other minor typos corrected. v3: Minor corrections, published version
- Subjects :
- General Mathematics
Categorification
Lattice (group)
01 natural sciences
Combinatorics
symbols.namesake
Mathematics::Category Theory
Mathematics - Quantum Algebra
0103 physical sciences
Frobenius algebra
FOS: Mathematics
Quantum Algebra (math.QA)
0101 mathematics
Representation Theory (math.RT)
Mathematics
010102 general mathematics
Monoidal category
Mathematics - Rings and Algebras
16. Peace & justice
Superalgebra
18D10 (Primary), 17B10, 17B65, 19A22 (Secondary)
Wreath product
Rings and Algebras (math.RA)
symbols
Grothendieck group
010307 mathematical physics
Mathematics - Representation Theory
Affine Hecke algebra
Subjects
Details
- Database :
- OpenAIRE
- Accession number :
- edsair.doi.dedup.....4eb3e363e499492fba066bde5fbaa248
- Full Text :
- https://doi.org/10.48550/arxiv.1507.06298