退化Heisenberg范畴及其Grothendieck环
The degenerate Heisenberg category and its Grothendieck ring
AI总结：
本研究证明了Khovanov提出的k=-1情形下退化Heisenberg范畴的加法Karoubi包的Grothendieck环与对应Heisenberg李代数泛包络代数的ℤ-形式同构的猜想，并将其推广到任意整数中心荷，还给出了余乘法的范畴化方法。
摘要：
退化Heisenberg范畴$\u210beis_k$是严格幺半范畴，其$k=-1$的特例最初由Khovanov于2010年提出。Khovanov猜想其范畴的加法Karoubi包的Grothendieck环同构于中心荷取$-1$的无限维Heisenberg李代数泛包络代数的某$\u2124$-形式。我们证明了该猜想，并将其推广到任意中心荷$k \u2208 \u2124$。我们还阐释了（一般情形下）余乘法的范畴化方法。
英文摘要：
The degenerate Heisenberg category $\mathcal{H}eis_k$ is a strict monoidal category which was originally introduced in the special case $k=-1$ by Khovanov in 2010. Khovanov conjectured that the Grothendieck ring of the additive Karoubi envelope of his category is isomorphic to a certain $\mathbb{Z}$-form for the universal enveloping algebra of the infinite-dimensional Heisenberg Lie algebra specialized at central charge $-1$. We prove this conjecture and extend it to arbitrary central charge $k \in \mathbb{Z}$. We also explain how to categorify the comultiplication (generically).
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
