Displaying similar documents to “Multipliers for the Hecke Algebra of a Real Semi Simple Lie Group”

Hom-structures on semi-simple Lie algebras

Wenjuan Xie, Quanqin Jin, Wende Liu (2015)

Open Mathematics

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A Hom-structure on a Lie algebra (g,[,]) is a linear map σ W g σ g which satisfies the Hom-Jacobi identity: [σ(x), [y,z]] + [σ(y), [z,x]] + [σ(z),[x,y]] = 0 for all x; y; z ∈ g. A Hom-structure is referred to as multiplicative if it is also a Lie algebra homomorphism. This paper aims to determine explicitly all the Homstructures on the finite-dimensional semi-simple Lie algebras over an algebraically closed field of characteristic zero. As a Hom-structure on a Lie algebra is not necessarily...

Control systems on semi-simple Lie groups and their homogeneous spaces

Velimir Jurdjevic, Ivan Kupka (1981)

Annales de l'institut Fourier

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In the present paper, we consider the class of control systems which are induced by the action of a semi-simple Lie group on a manifold, and we give a sufficient condition which insures that such a system can be steered from any initial state to any final state by an admissible control. The class of systems considered contains, in particular, essentially all the bilinear systems. Our condition is semi-algebraic but unlike the celebrated Kalman criterion for linear systems, it is not...