Results 211 to 220 of about 107,381 (262)
Some of the next articles are maybe not open access.
Deformations of Lie group and Lie algebra representations
Journal of Mathematical Physics, 1993A complete study of deformations of Lie group and Lie algebra representations, including differentiability and integrability results, is given. Adapted results are given in the semisimple case. A notion of induced deformations is introduced. Various examples are given, including deformations of indecomposable representations.
Lesimple, Marc, Pinczon, Georges
openaire +4 more sources
Lie Groups and Their Lie Algebras
2003In this chapter we apply the tools developed in Chapters 17–19 (flows, Lie derivatives, and foliations) to delve deeper into the relationships between Lie groups and Lie algebras.
openaire +2 more sources
2011
A Lie group is a manifold that is also a group such that the group operations are smooth. Classical groups such as the general and special linear groups over ℝ and over ℂ, orthogonal groups, unitary groups, and symplectic groups are all Lie groups.
openaire +2 more sources
A Lie group is a manifold that is also a group such that the group operations are smooth. Classical groups such as the general and special linear groups over ℝ and over ℂ, orthogonal groups, unitary groups, and symplectic groups are all Lie groups.
openaire +2 more sources
2012
We have studied linear transformation on \({\mathbb{R}}^{n}\) using the traditional matrix formalism in Chap. 7 and more generally in Chaps. 8–10, using the machinery of geometric algebra. This chapter explains the bivector interpretation of a general linear operator and offers a new proof of the Cayley–Hamilton theorem based upon this interpretation.
openaire +2 more sources
We have studied linear transformation on \({\mathbb{R}}^{n}\) using the traditional matrix formalism in Chap. 7 and more generally in Chaps. 8–10, using the machinery of geometric algebra. This chapter explains the bivector interpretation of a general linear operator and offers a new proof of the Cayley–Hamilton theorem based upon this interpretation.
openaire +2 more sources
2014
The notion of group—‘concrete’ as a group of transformations of a set or system of differential equations – goes back to the eigthteenth century.
openaire +2 more sources
The notion of group—‘concrete’ as a group of transformations of a set or system of differential equations – goes back to the eigthteenth century.
openaire +2 more sources
Lectures on Lie Groups and Lie Algebras: Simple groups of Lie type
, 1995R. Carter +3 more
semanticscholar +1 more source
Lie Algebras, Lie Groups, and Algebra of Incidence
2018We have learned that readers of the work of D. Hestenes and G. Sobzyk (Hestenes and Sobczyk (1984). Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics.) [138] Chap. 8 and a late article of Ch. Doran, D. Hestenes and F. Sommen (Doran, Hestenes, Sommen and Van Acker (1993).
openaire +2 more sources
1996
The first part of this chapter treats Lie algebras, beginning with definitions and many examples. The notions of solvable, nilpotent, radical, semisimple, and simple are introduced, and these notions are followed by a discussion of the effect of a change of the underlying field.
openaire +2 more sources
The first part of this chapter treats Lie algebras, beginning with definitions and many examples. The notions of solvable, nilpotent, radical, semisimple, and simple are introduced, and these notions are followed by a discussion of the effect of a change of the underlying field.
openaire +2 more sources