Results 11 to 20 of about 85,352 (227)
Discovering sparse representations of Lie groups with machine learning
Physics Letters B, 2023 Recent work has used deep learning to derive symmetry transformations, which preserve conserved quantities, and to obtain the corresponding algebras of generators. In this letter, we extend this technique to derive sparse representations of arbitrary Lie
Roy T. Forestano +5 more
doaj +1 more source
Topological loops with solvable multiplication groups of dimension at most six are centrally nilpotent [PDF]
International Journal of Group Theory, 2020 The main result of our consideration is the proof of the centrally nilpotency of class two property for connected topological proper loops $L$ of dimension $\le 3$ which have an at most six-dimensional solvable indecomposable Lie group as their ...
Agota Figula, Ameer Al-Abayechi
doaj +1 more source
Deformations of Yang-Baxter operators via n-Lie algebra cohomology
Nuclear Physics B, 2023 We introduce a cohomology theory of n-ary self-distributive objects in the tensor category of vector spaces that classifies their infinitesimal deformations.
Mohamed Elhamdadi, Emanuele Zappala
doaj +1 more source
Some results on L-dendriform algebras [PDF]
, 2010 We introduce a notion of L-dendriform algebra due to several different motivations. L-dendriform algebras are regarded as the underlying algebraic structures of pseudo-Hessian structures on Lie groups and the algebraic structures behind the $\mathcal O ...
Aguiar +24 more
core +2 more sources
Construction of Nilpotent and Solvable Lie Algebra in Picture Fuzzy Environment
International Journal of Computational Intelligence Systems, 2023 The picture fuzzy set was introduced by Coung. It is a generalization of the intuitionistic fuzzy set, giving the notion of neutral membership degrees along with the positive and negative ones.
Sajida Kousar +3 more
doaj +1 more source
Transitive Lie algebras of vector fields---an overview [PDF]
, 2011 This overview paper is intended as a quick introduction to Lie algebras of vector fields. Originally introduced in the late 19th century by Sophus Lie to capture symmetries of ordinary differential equations, these algebras, or infinitesimal groups, are ...
Draisma, Jan
core +3 more sources
Lie algebras whose Lie groups have negative sectional curvature
Revista Integración, 2022 The aim of this work is to completely describe two families of Lie algebras whose Lie groups have negative sectional curvature. The first family consists of Lie algebras satisfying the following property: given any two vectors in the Lie algebra, the ...
Gil Salgado
doaj
Some Problems in the Representation Theory of Simple Modular Lie Algebras [PDF]
, 2015 The finite-dimensional restricted simple Lie algebras of characteristic p > 5 are classical or of Cartan type. The classical algebras are analogues of the simple complex Lie algebras and have a well-advanced representation theory with important ...
Benkart, Georgia, Feldvoss, Jörg
core +3 more sources
Finite-dimensional Lie subalgebras of algebras with continuous inversion [PDF]
, 2008 We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition.
Beltita, Daniel, Neeb, Karl-Hermann
core +1 more source
Pro-Lie Groups: A Survey with Open Problems
Axioms, 2015 A topological group is called a pro-Lie group if it is isomorphic to a closed subgroup of a product of finite-dimensional real Lie groups. This class of groups is closed under the formation of arbitrary products and closed subgroups and forms a complete ...
Karl H. Hofmann, Sidney A. Morris
doaj +1 more source