Semigroups in symmetric Lie groups

Lie Groups. Representation Theory and Symmetric Spaces

INEXTENSIBLE FLOWS OF CURVES IN LIE GROUPS

In this paper, we study inextensible ows in three dimensional Lie groups with a bi-invariant metric. The necessary and sucient conditions for inextensible curve ow are expressed as a partial dierential equation involving the curvatures. Also, we give some results for special cases of Lie groups.

Lie Semigroups with Triple Decompositions

In this paper we establish that the causal order determined by an Ol’shanski semigroup on the corresponding homogeneous space is globally hyperbolic. Using this fact, we present sufficient conditions for a special class of Lie semigroups to admit a canonical “triple decomposition,” namely those for which the Lie algebra is of Cayley type. This theory applies in particular to semigroups which ar...

Lie Algebras, Algebraic Groups, and Lie Groups

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...

SEMINAR ON LIE GROUPS 1. Lie Groups

Example 1.3. (R,+) Example 1.4. S or T n = S × ...× S Example 1.5. Gl (n,F) ⊆ F, where F = R or C Example 1.6. E3 = isometries of R (2 connected components) Let the orthogonal group O3 < E3 be the subgroup that fixes the origin, and let the special orthogonal group SO (3) = SO3 < O3 be the orientation-preserving elements of O3. Visualizing SO (3): Let u be a vector of length l in R, correspondi...