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arXiv 2104.075302021-04-15math.QAmath.RT

椭圆 Hall 代数的范畴化

Categorification of the elliptic Hall algebra

Youssef Mousaaid, Alistair Savage

备注：: 36 pages
发表信息：: Documenta Mathematica 27 (2022), 1225-1273
DOI：: 10.25537/dm.2022v27.1225-1273

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AI总结：

本文建立椭圆 Hall 代数泛中心扩张的中心荷 $k$ 约化与量子 Heisenberg 范畴迹之间的同构，并据此构造其大量表示。

摘要：

我们证明，椭圆 Hall 代数的泛中心扩张在中心荷 $k$ 约化后，同构于中心荷为 $k$ 的量子 Heisenberg 范畴的迹，即零阶 Hochschild 同调。作为应用，我们构造了椭圆 Hall 代数泛中心扩张的大量表示族。

英文摘要：

We show that the central charge $k$ reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge $k$. As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.

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