Conjugacy classes in linear groups
N. Burgoyne,Richard Cushman +1 more
103
TL;DR: In this article, a simple and effective method for finding all conjugacy classes of G and all orbits of G in Lie Algebra is presented, and the splitting of classes and orbits when G is replaced by a normal subgroup is discussed.
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About: This article is published in Journal of Algebra. The article was published on 01 Feb 1977. and is currently open access. The article focuses on the topics: Conjugacy class & Normal subgroup.
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Citations
Reversible Equivariant Linear Systems
Jeroen S. W. Lamb,Mark Roberts +1 more
TL;DR: In this article, the authors classify the structure of linear reversible systems (vector fields) on Rn that are equivariant with respect to a linear representation of a compact Lie group H. The main tool for the classification is the representation theory of compact Lie groups.
41
Versal Deformations and Normal Forms for Reversible and Hamiltonian Linear Systems
TL;DR: In this paper, the equivalence classes and their versal deformations for reversible and reversible Hamiltonian matrices are characterized by signs, and the main tool in the characterization is reduction to the semi Simple case.
37
Normal forms and versal deformations of linear Hamiltonian systems
Hüseyi̇in Koçak,Hüseyi̇in Koçak +1 more
TL;DR: In this article, Versal deformations of real Hamiltonian systems in normal form are constructed for the study of bifurcations of linear systems with small codimension.
36
References
•Book
Differential Geometry and Symmetric Spaces
Sigurdur Helgason
- 01 Jan 1962
TL;DR: In this article, the classification of symmetric spaces has been studied in the context of Lie groups and Lie algebras, and a list of notational conventions has been proposed.
On the conjugacy classes in the unitary, symplectic and orthogonal groups
TL;DR: In this article, the determinacy of conjugacy classes in finite-dimensional unitary, symplectic and orthogonal groups over division rings or fields has been studied, and the equivalence classes of non-degenerate sesquilinear forms on finite dimensional vector spaces.
On a normal form of the orthogonal transformation III
TL;DR: In this paper, the distribution of the characteristic roots of the linear transformations that leave invariant the quadratic form t2+x2-y2-z2, just as one knows that a Lorentz transformation has two complex conjugate characteristic roots and two real characteristic roots that are either inverse to one another or the numbers 1 and 1.
Normal Matrices Over an Arbitrary Field of Characteristic Zero
TL;DR: In this paper, the authors considered the problem of finding the canonical form of a normal matrix A under unitary transformation, where the matrices under consideration are matrices over a field of characteristic zero, and gave necessary and sufficient conditions that two matrices, both normal with respect to H, be similar under transformations by matrices which are conjunctive automorphs of H.
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