Projects per year
Abstract
Let g be a semisimple Lie algebra over the field of real numbers. Let G be a real Lie group with Lie algebra g. The real Weyl group of G with respect to a Cartan subalgebra h of g is defined as W(G,h)=N_{G}(h)/Z_{G}(h). We describe an explicit construction of W(G,h) for Lie groups G that arise as the set of real points of connected algebraic groups. We show that this also gives a construction of W(G,h) when G is the adjoint group of g. This algorithm is important for the classification of regular semisimple subalgebras, real carrier algebras, and real nilpotent orbits associated with g; the latter have various applications in theoretical physics.
Original language  English 

Pages (fromto)  114 
Number of pages  14 
Journal  Journal of Symbolic Computation 
Volume  104 
DOIs  
Publication status  Published  May 2021 
Keywords
 Computational Lie theory
 Real semisimple Lie algebra
 Real Weyl group
Projects
 1 Finished

Computing with Lie groups and algebras: nilpotent orbits and applications
Dietrich, H. & de Graaf, W. A.
1/04/19 → 31/01/23
Project: Research