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Transitive actions of semigroups in semi-simple Lie groups (1999)

San Martin, L.A.B. ; Tonelli, P.A.

Springer

Semigroup forum 58 (1999), S. 142-151

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ISSN: 1432-2137

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: G be a connected semi-simple Lie group with finite center and S⊂G a semigroup with interior points. It is proved that S is transitive on a homogenous space G/L only if the action of L on B is minimal and contracting, where B=G/Pis the flag manifold of G asssociated with S. In [5, Thm.6.4] the authors claimed another necessary condition in case G is simple, namely, that L is discrete. It is shown by means of an example that this condition is wrong without the further assumption that G/L is compact.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s002339900004

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