A Note On Heisenberg Categorification
Na Wang, Zhixi Wang, Ke Wu, Jie Yang, and Zifeng Yang
TL;DR
This paper discusses a categorification of the Heisenberg algebra using graphical calculus, proving a conjecture relating it to the Grothendieck ring through a categorification of a deformed algebra.
Contribution
It provides a proof of Khovanov's conjecture by establishing an isomorphism between the Heisenberg algebra and the Grothendieck ring of a categorified algebra.
Findings
Proof of Khovanov's conjecture established
Categorification of a deformed Heisenberg algebra demonstrated
Connection between algebra and Grothendieck ring confirmed
Abstract
A categorification of the Heisenberg algebra is constructed in by Khovanov using graphical calculus, and left with a conjecture on the isomorphism between the Heisenberg algebra and Grothendieck ring of the constructed category. We give a proof of Khovanov's conjectured statement in this paper from a categorification of some deformed Heisenberg algebra.
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Taxonomy
TopicsComplex Systems and Time Series Analysis · Mathematical Dynamics and Fractals