Results 21 to 30 of about 852 (252)

On the centroid of Heisenberg Lie algebra

四川大学学报. 自然科学版, 2023
Heisenberg Lie algebra belongs to a class of solvable Lie algebra. It has a deep physical background and thus is an important object of Lie algebra study.
YU De-Ming, MA Jie-Jing, JIANG Chan
doaj  

Controllability of Linear Systems on Solvable Lie Groups [PDF]

SIAM Journal on Control and Optimization, 2016
Linear systems on Lie groups are a natural generalization of linear system on Euclidian spaces. For such systems, this paper studies controllability by taking in consideration the eigenvalues of an associated derivation D. When the state space is a solvable connected Lie group, controllability of the systems is guaranteed if the reachable set of the ...
openaire   +3 more sources

On the extensions of infinite-dimensional representations of Lie semigroups

International Journal of Mathematics and Mathematical Sciences, 2002
The necessary and sufficient conditions have been obtained for extendability of a Banach representation of a generating Lie semigroup S to a local representation of the Lie group G generated by S when the tangent wedge of S is a Lie semialgebra. The most
Adolf R. Mirotin
doaj   +1 more source

From homogeneous metric spaces to Lie groups

Comptes Rendus. Mathématique
We study homogeneous metric spaces, by which we mean connected, locally compact metric spaces whose isometry group acts transitively.After a review of a number of classical results, we use the Gleason–Iwasawa–Montgomery–Yamabe–Zippin structure theory to ...
Cowling, Michael G., Kivioja, Ville, Le Donne, Enrico, Nicolussi Golo, Sebastiano, Ottazzi, Alessandro   +4 more
doaj   +1 more source

On Translation Curves and Geodesics in ${\mathrm{Sol}}_1^4$

Mathematics, 2023
A translation curve in a homogeneous space is a curve such that for a given unit vector at the origin, translation of this vector is tangent to the curve in its every point.
Zlatko Erjavec, Marcel Maretić
doaj   +1 more source

Geodesics and Translation Curves in ${\mathrm{Sol}}_0^4$

Mathematics, 2023
A translation curve in a Thurston space is a curve such that for given unit vector at the origin, the translation of this vector is tangent to the curve in every point of the curve. In most Thurston spaces, translation curves coincide with geodesic lines.
Zlatko Erjavec
doaj   +1 more source

An extention of Nomizu’s Theorem –A user’s guide–

Complex Manifolds, 2016
For a simply connected solvable Lie group G with a lattice Γ, the author constructed an explicit finite-dimensional differential graded algebra A*Γ which computes the complex valued de Rham cohomology H*(Γ\G, C) of the solvmanifold Γ\G.
Kasuya Hisashi
doaj   +1 more source

Exponential Radicals of Solvable Lie Groups

Journal of Algebra, 2002
For any connected Lie group \(G\), we consider the metric induced by some left-invariant Riemannian structure on \(G\). An element \(g\) of \(G\) is said to be strictly exponentially distorted in \(G\) if the length of \(g^n\) in \(G\) grows as \(\log(|n|+ 1)\).
openaire   +1 more source

Modelling stem cell differentiation related processes—A practical overview for biologists

FEBS Letters, EarlyView.
Stem cell differentiation is complex and difficult to control experimentally. This review introduces suitable computational modelling approaches that can support stem cell research, from mechanistic ODE and abstract models to multiscale and deep learning methods.
Ricco Zeegelaar, Xinqi Yan, Lucas F. Jansen Klomp, Stefano Schivo, Janine N. Post   +4 more
wiley   +1 more source

Solvability and Nilpotency of Lie Algebras in Cryptography and Steganography

Mathematics
This paper investigates the role of solvable and nilpotent Lie algebras in the domains of cryptography and steganography, emphasizing their potential in enhancing security protocols and covert communication methods.
Amor Hasić, Melisa Azizović, Emruš Azizović, Muzafer Saračević   +3 more
doaj   +1 more source