The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Displaying similar documents to “On two results of Singhof”

Classification of connected unimodular Lie groups with discrete series

Anh Nguyen Huu (1980)

Annales de l'institut Fourier

Similarity:

We introduce a new class of connected solvable Lie groups called H -group. Namely a H -group is a connected solvable Lie group with center Z such that for some in the Lie algebra h of H , the symplectic for B on h / z given by ( [ x , y ] ) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z , such that the center of G / Rad G is finite, has discrete series if and only if G may be written as G = H S ' , H S = Z 0 , where H is a H -group with...

Recollement of colimit categories and its applications

Ju Huang, QingHua Chen, Chunhuan Lai (2020)

Czechoslovak Mathematical Journal

Similarity:

We give an explicit recollement for a cocomplete abelian category and its colimit category. We obtain some applications on Leavitt path algebras, derived equivalences and K -groups.

Triple automorphisms of simple Lie algebras

Deng Yin Wang, Xiaoxiang Yu (2011)

Czechoslovak Mathematical Journal

Similarity:

An invertible linear map ϕ on a Lie algebra L is called a triple automorphism of it if ϕ ( [ x , [ y , z ] ] ) = [ ϕ ( x ) , [ ϕ ( y ) , ϕ ( z ) ] ] for x , y , z L . Let 𝔤 be a finite-dimensional simple Lie algebra of rank l defined over an algebraically closed field F of characteristic zero, 𝔭 an arbitrary parabolic subalgebra of 𝔤 . It is shown in this paper that an invertible linear map ϕ on 𝔭 is a triple automorphism if and only if either ϕ itself is an automorphism of 𝔭 or it is the composition of an automorphism of 𝔭 and an extremal map of order 2 . ...

Invariant orders in Lie groups

Neeb, Karl-Hermann

Similarity:

[For the entire collection see Zbl 0742.00067.]The author formulates several theorems about invariant orders in Lie groups (without proofs). The main theorem: a simply connected Lie group G admits a continuous invariant order if and only if its Lie algebra L ( G ) contains a pointed invariant cone. V. M. Gichev has proved this theorem for solvable simply connected Lie groups (1989). If G is solvable and simply connected then all pointed invariant cones W in L ( G ) are global in G (a Lie wedge W L ( G ) ...