Homotopy Lie theory: Lie's Second Theorem for Lie $n$-groupoids
Final Report Abstract
This research project embarks on a fascinating exploration at the crossroads of algebraic realms, specifically delving into the intriguing interplay between Lie n-groupoids and Lie n-algebroids, with a central focus on unraveling the intricacies encapsulated in Lie’s Second Theorem. The core emphasis rests on cultivating a profound comprehension of the intricate relationships that bind these mathematical entities, and this exploration gains depth through the nuanced lenses of differentiation and integration processes. Essentially, we’re exploring how these algebraic structures are connected and trying to make sense of their relationships by looking at processes like differentiation and integration - concepts one might remember from calculus. As the research unfolds, it delves into the rich tapestry of homotopy aspects within Lie theory, striving to unearth the hidden connections and profound implications inherent in Lie n-groupoids and Lie n-algebroids within the broader landscape of higher categorical algebraic structures. Beyond the pursuit of elucidating Lie’s Second Theorem within this intricate framework, the investigation aspires to contribute meaningfully to the expansive realm of homotopy Lie theory, propelling the collective understanding of these mathematical structures to new heights.
Publications
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Chern–Simons, Wess–Zumino and other cocycles from Kashiwara–Vergne and associators. Letters in Mathematical Physics, 108(3), 757-778.
Alekseev, Anton; Naef, Florian; Xu, Xiaomeng & Zhu, Chenchang
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Topological nonlinear σ -model, higher gauge theory, and a systematic construction of 3+1D topological orders for boson systemss. Physical Review B, 100(4).
Zhu, Chenchang; Lan, Tian & Wen, Xiao-Gang
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On the homotopy theory for Lie ∞–groupoids, with an application to integrating L∞–algebras. Algebraic & Geometric Topology, 20(3), 1127-1219.
Rogers, Christopher & Zhu, Chenchang
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The Controlling $$L_\infty $$-Algebra, Cohomology and Homotopy of Embedding Tensors and Lie–Leibniz Triples. Communications in Mathematical Physics, 386(1), 269-304.
Sheng, Yunhe; Tang, Rong & Zhu, Chenchang
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Shifted symplectic higher Lie groupoids and classifying spaces. Advances in Mathematics, 413, 108829.
Cueca, Miquel & Zhu, Chenchang
