Corpus ID: 233482015

Representation of Real Solvable Lie Algebras Having 2-dimensional Derived Ideal and Geometry of Coadjoint Orbits of Corresponding Lie Groups

@inproceedings{Nguyen2021RepresentationOR,
  title={Representation of Real Solvable Lie Algebras Having 2-dimensional Derived Ideal and Geometry of Coadjoint Orbits of Corresponding Lie Groups},
  author={Tu T. C. Nguyen and Vu Anh Le},
  year={2021}
}
Given a Lie algebra G, let μ(G) be the minimal degree of a faithful representation of G. This is an integer valued invariant of G, which has been introduced by D. Burde [3] in 1998. It is not known, in general, how to determine this invariant for a given solvable Lie algebra. Lie (n, k) denotes the class of all n-dimensional real solvable Lie algebras having k-dimensional derived ideals. In 2020 we [18] gave a classification of all non 2-step nilpotent Lie algebras of Lie (n, 2). We propose in… Expand

Tables from this paper

References

SHOWING 1-10 OF 42 REFERENCES
A classification of real finite-dimensional lie algebras with a low-dimensional derived algebra
Abstract Real n -dimensional Lie algebras with a 1-, 2- and 3-dimensional derived algebra are classified. Lie algebras with a 1-dimensional derived algebra are classified completely, for Lie algebrasExpand
Solvable Lie A-algebras
A finite-dimensional Lie algebra $L$ over a field $F$ is called an $A$-algebra if all of its nilpotent subalgebras are abelian. This is analogous to the concept of an $A$-group: a finite group withExpand
Minimal representations for 6-dimensional nilpotent Lie algebra
Given a Lie algebra 𝔤, let μ(𝔤) and μnil(𝔤) be the minimal dimension of a faithful representation and nilrepresentation of 𝔤, respectively. In this paper, we give μ(𝔤) and μnil(𝔤) for eachExpand
ON UNITARY REPRESENTATIONS OF NILPOTENT LIE GROUPS.
  • J. Dixmier
  • Mathematics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • 1957
IThis follows from Theorem 1 in D. Montgomery, H. Samelson, and L. Zippin, "Singular Points of a Compact Transformation Group," Ann. Math., 63, 1-9, 1956. 2 E. Spanier and H. H. C. Whitehead, "OnExpand
On a refinement of Ado's theorem
Abstract. In this paper we study the minimal dimension $ \mu (g) $ of a faithful g-module for n-dimensional Lie algebras g. This is an interesting invariant of g which is difficult to compute. It isExpand
Applying matrix theory to classify real solvable Lie algebras having 2-dimensional derived ideals
Abstract We present a new approach to the problem of classifying real solvable Lie algebras having 2-dimensional derived ideals. Partial results on this problem were obtained by Schobel in 1993 andExpand
Non-Commutative Geometry Methods for Group C*-Algebras
This research notes is intended to provide a quick introduction to the subject. We expose a K-theoretic approach to study group C*-algebras: started in the elementary part, with one example ofExpand
Minimal Faithful Representation of the Heisenberg Lie Algebra with Abelian Factor
For a finite dimensional Lie algebra $\g$ over a field $\k$ of characteristic zero, the $\mu$-function (respectively $\mu_{nil}$-function) is defined to be the minimal dimension of $V$ such that $\g$Expand
Minimal faithful representations of reductive Lie algebras
Abstract.We prove an explicit formula for the invariant $$\mu({\mathfrak{g}})$$ for finite-dimensional semisimple, and reductive Lie algebras $${\mathfrak{g}}$$ over $${\mathbb{C}}$$ . Here Expand
Minimal matrix representations of five-dimensional Lie algebras
We obtain minimal dimension matrix representations for each indecomposable five-dimensional Lie algebra over $\R$ and justify in each case that they are minimal. In each case a matrix Lie group isExpand
...
1
2
3
4
5
...