A semisimple subcategory of Khovanov's Heisenberg category

2025/12/16 by Sam K. Miller, Miller, Sam K.
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Operator Algebra Research

paper · pdf · doi:10.48550/arxiv.2512.13968

Abstract

We show the existence of a semisimple replete subcategory of Khovanov's Heisenberg category that retains the isomorphism data of objects for the full category. This leads to a noncommutative tensor-triangular geometric example of a monoidal triangulated category whose Balmer spectrum satisfies the tensor product property but which contains one-sided thick tensor-ideals that are not two-sided, and whose standard support varieties fail to classify one-sided thick tensor-ideals.

Citations

• Noncommutative tensor triangular geometry: modules, bimodules, and unipotent Hopf algebras
• Re-framing the classification of ideals in noncommutative tensor-triangular geometry
• An update on Heisenberg and Kac-Moody categorification
• The homological spectrum for monoidal triangulated categories
• On functoriality and the tensor product property in noncommutative tensor-triangular geometry
• Group actions on monoidal triangulated categories and Balmer spectra
• Support varieties for finite tensor categories: the tensor product property
• Noncommutative tensor triangular geometry and the tensor product property for support maps
• Noncommutative tensor triangular geometry
• Heisenberg algebra and a graphical calculus

Related

• Re-framing the classification of ideals in noncommutative tensor-triangular geometry
• On functoriality and the tensor product property in noncommutative tensor-triangular geometry
• Noncommutative tensor triangular geometry
• A Note On Heisenberg Categorification
• Noncommutative tensor triangulated categories and coherent frames