Concept
Lie group–Lie algebra correspondence
Publications associées (72)
Hybrid ground-state quantum algorithms based on neural Schrödinger forging
Giuseppe Carleo, Sofia Vallecorsa
Entanglement forging based variational algorithms leverage the bipartition of quantum systems for addressing ground-state problems. The primary limitation of these approaches lies in the exponential summation required over the numerous potential basis stat ...
Amer Physical Soc2024Touch and Closeness in Naturally Organized Activities
Countless aspects of touch and closeness have been questioned in an unprecedented way during the recent Covid epidemic. Social practices as banal as greetings were both reflexively and practically challenged and sometimes deeply altered, resulting in painf ...
2024Lie groups in the symmetric group: Reducing Ulam's problem to the simple case
Ulam asked whether all Lie groups can be represented faithfully on a countable set. We establish a reduction of Ulam's problem to the case of simple Lie groups. In particular, we solve the problem for all solvable Lie groups and more generally Lie groups w ...
San Diego2023Geometric Algebra for Optimal Control With Applications in Manipulation Tasks
Many problems in robotics are fundamentally problems of geometry, which have led to an increased research effort in geometric methods for robotics in recent years. The results were algorithms using the various frameworks of screw theory, Lie algebra, and d ...
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2023Lie groups as permutation groups: Ulam's problem in the nilpotent case
Ulam asked whether every connected Lie group can be represented on a countable structure. This is known in the linear case. We establish it for the first family of non-linear groups, namely in the nilpotent case. Further context is discussed to illustrate ...
WALTER DE GRUYTER GMBH2022On minimal tilting complexes in highest weight categories
We explain the construction of minimal tilting complexes for objects of highest weight categories and we study in detail the minimal tilting complexes for standard objects and simple objects. For certain categories of representations of complex simple Lie ...
2022The algebra of Boolean matrices, correspondence functors, and simplicity
We determine the dimension of every simple module for the algebra of the monoid of all relations on a finite set (i.e. Boolean matrices). This is in fact the same question as the determination of the dimension of every evaluation of a simple correspondence ...
2020