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1. Simple 𝑝-adic Lie groups with abelian Lie algebras

   https://doi.org/10.1515/crelle-2024-0030  

   Caprace, Pierre-Emmanuel; Minasyan, Ashot; Osin, Denis (June 2024, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract For each prime 𝑝 and each positive integer 𝑑, we construct the first examples of second countable, topologically simple 𝑝-adic Lie groups of dimension 𝑑 whose Lie algebras are abelian.This answers several questions of Glöckner and Caprace–Monod.The proof relies on a generalization of small cancellation methods that applies to central extensions of acylindrically hyperbolic groups. 

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2. Lie Algebraic Cost Function Design for Control on Lie Groups

   Sangli Teng, William Clark (January 2022, Proc. IEEE CDC 2022)

   This paper presents a control framework on Lie groups by designing the control objective in its Lie algebra. Control on Lie groups is challenging due to its nonlinear nature and difficulties in system parameterization. Existing methods to design the control objective on a Lie group and then derive the gradient for controller design are non-trivial and can result in slow convergence in tracking control. We show that with a proper left-invariant metric, setting the gradient of the cost function as the tracking error in the Lie algebra leads to a quadratic Lyapunov function that enables globally exponential convergence. In the PD control case, we show that our controller can maintain an exponential convergence rate even when the initial error is approaching π in SO(3). We also show the merit of this proposed framework in trajectory optimization. The proposed cost function enables the iterative Linear Quadratic Regulator (iLQR) to converge much faster than the Differential Dynamic Programming (DDP) with a well-adopted cost function when the initial trajectory is poorly initialized on SO(3). 

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3. Lie Algebra Canonicalization: Equivariant Neural Operators under arbitrary Lie Groups

   Shumaylov, Z; Zaika, P; Rowbottom, J; Sherry, F; Weber, M; Schönlieb, C-B (May 2025, International Conference on Learning Representations)
4. It Takes Two to Lie: One to Lie, and One to Listen

   Denis Peskov, Benny Cheng (January 2020, Proceedings of ACL)

   Trust is implicit in many online text conversations—striking up new friendships, or asking for tech support. But trust can be betrayed through deception. We study the language and dynamics of deception in the negotiation-based game Diplomacy, where seven players compete for world domination by forging and breaking alliances with each other. Our study with players from the Diplomacy community gathers 17,289 messages annotated by the sender for their intended truthfulness and by the receiver for their perceived truthfulness. Unlike existing datasets, this captures deception in long-lasting relationships, where the interlocutors strategically combine truth with lies to advance objectives. A model that uses power dynamics and conversational contexts can predict when a lie occurs nearly as well as human players. 

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5. Efficient Reachable Sets on Lie Groups Using Lie Algebra Monotonicity and Tangent Intervals

   https://doi.org/10.1109/CDC56724.2024.10886065  

   Harapanahalli, Akash; Coogan, Samuel (December 2024, IEEE)