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arXiv · 2507.09438

Quantum BV $\mathcal{L}_{\infty}$-algebras I: Derived geometric foundations

Elliot Cheung
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Abstract

We introduce the concept of a quantum BV $\mathcal{L}_{\infty}$-algebra and study fundamental properties. In particular, we investigate homotopy Lie theoretic structures that naturally arise in the context of Chern-Simons theory. Of note, are the notions of homotopy BV data and of a BV orientation. The sequel of this paper will involve the direct application of these constructions to the setting of Chern-Simons theory.

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BibTeXRIS

Elliot Cheung. 2025-07-13. Quantum BV $\mathcal{L}_{\infty}$-algebras I: Derived geometric foundations. https://arxiv.org/abs/2507.09438

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