论文标题
奇数环形纳坦类别和GL（1 | 1）
Odd annular Bar-Natan category and gl(1|1)
论文作者
论文摘要
我们介绍了两个单体超级类别：奇数点templey-lieb类别$ \ MATHCAL {t \！l} _ {o，\ bulter}（δ）$，这是Brundan和Ellis和Odd Annular Bar-Natan的奇数temperley-lieb类别的概括。 $ \ MATHCAL {Bn} _ {\！o}（\ Mathbb {a}）$，它概括了Putyra研究的奇数bar-natan类别。然后，如果$δ= 0 $，我们表明它们之间存在类别的等效性。我们使用这种等价来更好地理解谎言superalgebra $ \ mathfrak {gl}（1 | 1）$在格里格斯比（Grigsby）和第二作者发现的厚实的安努鲁斯（Annulus）中的奇数khovanov同源性上。
We introduce two monoidal supercategories: the odd dotted Temperley-Lieb category $\mathcal{T\!L}_{o,\bullet}(δ)$, which is a generalization of the odd Temperley-Lieb category studied by Brundan and Ellis, and the odd annular Bar-Natan category $\mathcal{BN}_{\!o}(\mathbb{A})$, which generalizes the odd Bar-Natan category studied by Putyra. We then show there is an equivalence of categories between them if $δ=0$. We use this equivalence to better understand the action of the Lie superalgebra $\mathfrak{gl}(1|1)$ on the odd Khovanov homology of a knot in a thickened annulus found by Grigsby and the second author.
