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arXiv 2109.034102021-09math.RT

P型网

Webs of Type P

Nicholas Davidson, Jonathan R. Kujawa, Robert Muth

备注：: Final version. Compared to the first version, there are no substantive changes to the mathematics, but numerous changes to exposition in response to referee suggestions. Updated authors' affiliations
发表信息：: Can. J. Math.-J. Can. Math. 76 (2024) 1917-1966
DOI：: 10.4153/S0008414X23000688

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AI总结：

本文引入了P型网超范畴，通过生成元与关系将其定义为图示幺单k-线性超范畴，研究了其结构并给出态射空间的图示基，证明其为P型李超代数自然模对称幂生成的幺单超范畴提供了组合模型。

摘要：

本文引入了P型网超范畴。它们通过生成元和关系被定义为图示幺半k-线性超范畴。我们研究了这些范畴的结构，并为其态射空间提供了图示基。我们还证明了这些超范畴为P型李超代数的自然模及其对偶的对称幂所生成的幺半超范畴提供了组合模型。

英文摘要：

This paper introduces type P web supercategories. They are defined as diagrammatic monoidal $k$-linear supercategories via generators and relations. We study the structure of these categories and provide diagrammatic bases for their morphism spaces. We also prove these supercategories provide combinatorial models for the monoidal supercategory generated by the symmetric powers of the natural module and their duals for the Lie superalgebra of type P.

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