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arXiv · 2108.07919

Generators for K-theoretic Hall algebras of quivers with potential

Tudor Pădurariu
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Abstract

K-theoretic Hall algebras (KHAs) of quivers with potential $(Q,W)$ are a generalization of preprojective KHAs of quivers, which are conjecturally positive parts of the Okounkov-Smironov quantum affine algebras. In particular, preprojective KHAs are expected to satisfy a Poincar\'e-Birkhoff-Witt theorem. We construct semi-orthogonal decompositions of categorical Hall algebras using techniques developed by Halpern-Leistner, Ballard-Favero-Katzarkov, and \v{S}penko-Van den Bergh. For a quotient of $\text{KHA}(Q,W)_{\mathbb{Q}}$, we refine these decompositions and prove a PBW-type theorem for it. The spaces of generators of $\text{KHA}(Q,0)_{\mathbb{Q}}$ are given by (a version of) intersection K-theory of coarse moduli spaces of representations of $Q$.

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Tudor Pădurariu. 2021-08-18. Generators for K-theoretic Hall algebras of quivers with potential. https://arxiv.org/abs/2108.07919

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