# A note on semidirect sum of Lie algebras

@article{Ostrowski2013ANO, title={A note on semidirect sum of Lie algebras}, author={Tadeusz Marian Ostrowski}, journal={Discussiones Mathematicae General Algebra and Applications}, year={2013}, volume={33}, pages={233-247} }

In the paper there are investigated some properties of Lie algebras, the construction which has a wide range of applications like computer sciences (especially to computer visions), geometry or physics, for example. We concentrate on the semidirect sum of algebras and there are extended some theoretic designs as conditions to be a center, a homomorphism or a derivative. The Killing form of the semidirect sum where the second component is an ideal of the first one is considered as well.

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SHOWING 1-10 OF 33 REFERENCES

Lie groups and Lie algebras

- Mathematics
- 1998

From the reviews of the French edition "This is a rich and useful volume. The material it treats has relevance well beyond the theory of Lie groups and algebras, ranging from the geometry of regular…

LIE GROUPS AND LIE ALGEBRAS

- MathematicsLie Groups, Lie Algebras, and Cohomology. (MN-34), Volume 34
- 2021

The first example of a Lie group is the general linear group GL(n,R) = {A ∈ Matn(R)| det(A) 6= 0} of invertible n × n matrices. It is an open subset of Matn(R), hence a submanifold, and the…

Lie Groups and Algebras with Applications to Physics, Geometry and Mechanics

- Mathematics, Physics
- 1986

This is an introductory text on Lie groups and algebras and their roles in diverse areas of pure and applied mathematics and physics. The material is presented in a way that is at once intuitive,…

Wreath product of Lie algebras and Lie algebras associated with Sylow p-subgroups of ﬁnite symmetric groups

- Mathematics
- 2006

. We deﬁne a wreath product of a Lie algebra L with the one-dimensional Lie algebra L 1 over F p and determine some properties of this wreath product. We prove that the Lie algebra associated with…

Introduction to Lie algebras

- Mathematics
- 2006

Ideals and Homomorphisms.- Low-Dimensional Lie Algebras.- Solvable Lie Algebras and a Rough Classification.- Subalgebras of gl(V).- Engel's Theorem and Lie's Theorem.- Some Representation Theory.-…

Indecomposable Lie algebras with nontrivial Levi decomposition cannot have filiform radical

- Mathematics
- 2006

Let g = s n r be an indecomposable Lie algebra with nontrivial semisimple Levi subalgebra s and nontrivial solvable radical r. In this note it is proved that r cannot be isomorphic to a filiform…

Dimension Formulas for the Free Nonassociative Algebra

- Mathematics
- 2004

ABSTRACT The free nonassociative algebra has two subspaces which are closed under both the commutator and the associator: the Akivis elements and the primitive elements. Every Akivis element is…

The Euler–Poincaré Equations and Semidirect Products with Applications to Continuum Theories

- Mathematics
- 1998

We study Euler–Poincare systems (i.e., the Lagrangian analogue of Lie–Poisson Hamiltonian systems) defined on semidirect product Lie algebras. We first give a derivation of the Euler–Poincare…

Wreath products and Kaluzhnin-Krasner embedding for Lie algebras

- Mathematics
- 2006

The wreath product of groups A /B is one of basic constructions in group theory. We construct its analogue, a wreath product of Lie algebras. Consider Lie algebras H_and G over a field K. Let U(G) be…