Complex adjoint orbits in Lie theory and geometry
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DOI: 10.1016/j.exmath.2017.12.001
Abstract: This expository article is an introduction to the adjoint orbits of complex semisimple groups, primarily in the algebro-geometric and Lie-theoretic contexts, and with a pronounced emphasis on the properties of semisimple and nilpotent orbits. It… read more here.
Keywords: lie theory; orbits lie; complex adjoint; geometry ... See more keywords
Type-II neural symmetry detection with Lie theory
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DOI: 10.1038/s41598-025-17098-8
Abstract: Understanding symmetries within data is crucial for explainability and enhancing model efficiency in artificial intelligence. This work investigates an approach to neural symmetry detection, specifically leveraging the mathematical framework of Lie theory. Our approach projects… read more here.
Keywords: symmetry; neural symmetry; symmetry detection; lie theory ... See more keywords
Lie-theory-based dynamics modeling method of snake-arm robot with virtual linkage criterion
Sign Up to like & getrecommendations! Published in 2025 at "Journal of Mechanisms and Robotics"
DOI: 10.1115/1.4069153
Abstract: Cable-driven snake-arm robots with high degrees of freedom and flexible slender body are very suitable in applications to unstructured narrow situations. For the high-performance development of snake-arm robots, dynamics modeling is a very important issue,… read more here.
Keywords: snake arm; dynamics modeling; lie theory; arm robot ... See more keywords
Controllability of Bilinear Systems: Lie Theory Approach and Control Sets on Projective Spaces
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DOI: 10.3390/math13142273
Abstract: Bilinear systems can be developed from the point of view of time-varying linear differential equations or from the symmetry of Lie theory, in particular Lie algebras, Lie groups, and Lie semigroups. For bilinear control systems… read more here.
Keywords: system; control; controllability; control sets ... See more keywords