Automatic continuity of pseudocharacters on semisimple Lie groups

Shtern, A. I.

doi:10.1007/s11006-006-0157-9

Cited by 9 publications

(11 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It remains to show that it is non-trivial. In fact we show in Section 2.3 that it is equal to the Guichardet-Wigner [52,31,22,82,14] quasimorphism ̺ G on G by comparing them on π 1 (G) and arguing that a homogenous quasimorphism on G is determined by its restriction to the fundamental group.…”

Section: Finite Dimensional Examples: Guichardet-wigner Quasimorphismsmentioning

confidence: 97%

See 1 more Smart Citation

The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures

Shelukhin¹

2014

Comment. Math. Helv.

View full text Add to dashboard Cite

We extend the definition of Weinstein's Action homomorphism to Hamiltonian actions with equivariant moment maps of (possibly infinite-dimensional) Lie groups on symplectic manifolds, and show that under conditions including a uniform bound on the symplectic areas of geodesic triangles the resulting homomorphism extends to a quasimorphism on the universal cover of the group. We apply these principles to finite dimensional Hermitian Lie groups like the linear symplec-

show abstract

Section: Finite Dimensional Examples: Guichardet-wigner Quasimorphismsmentioning

confidence: 97%

“…We remark that as we have assumed that G has finite center, there are no homogenous quasimorphisms on G (cf. [82,15] and [7] for the group Sp(2n, R)). Moreover it is known that the all homogenous quasimorphisms on G are proportional to ̺ G (cf.…”

Section: Finite Dimensional Examples and Guichardet-wigner Quasimorphmentioning

confidence: 99%

The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures

Shelukhin¹

2014

Comment. Math. Helv.

View full text Add to dashboard Cite

show abstract

“…In the next theorem, which can be regarded as a proof of the physical meaningfulness of the notion of an irreducible unbounded finite-dimensional representation of a perfect Lie group, we combine the results of known theorems obtained in [20]- [24] and [52]- [57] with the results of the present paper.…”

Section: 2mentioning

confidence: 97%

A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups

Shtern¹

2008

Izv. Math.

View full text Add to dashboard Cite

“…[19,10,6]), in symplectic topology (see the recent survey [12] for references) and in the study of quasimorphisms on finite (see e.g. [20,7,22,8,2,3,9]) and infinite-dimensional (see e.g. [13,4,1,23]) Lie groups.…”

mentioning

confidence: 99%

Quasi-state rigidity for finite-dimensional Lie algebras

Björklund

Hartnick

2017

Isr. J. Math.

View full text Add to dashboard Cite

We say that a Lie algebra g is quasi-state rigid if every Ad-invariant continuous Lie quasi-state on it is the directional derivative of a homogeneous quasimorphism. Extending work of Entov and Polterovich, we show that every reductive Lie algebra, as well as the algebras C n u(n), n ≥ 1, are rigid. On the other hand, a Lie algebra which surjects onto the three-dimensional Heisenberg algebra is not rigid. For Lie algebras of dimension ≤ 3 and for solvable Lie algebras which split over a codimension one abelian ideal, we show that this is the only obstruction to rigidity. MICHAEL BJÖRKLUND AND TOBIAS HARTNICKis primarily interested in the infinite-dimensional case, such an analysis is relevant in order to understand the behaviour of Lie quasi-states along finite-dimensional subalgebras. However, to the best of our knowledge [15] remains the only paper so far which concerns Lie quasi-states on finite-dimensional Lie algebras.The purpose of the present paper is to extend some of the results from [15] to larger classes of finite-dimensional Lie algebras and to obtain a clearer picture about Lie quasi-states on general finite-dimensional Lie algebras through some key examples. Our main focus will be on Adinvariant Lie quasi-states, since these are comparatively easy to handle and at the same time the most relevant ones in applications. One particular goal of this article is to understand their connection with homogeneous quasimorphisms on finite-dimensional Lie groups. Integrable Lie quasi-states and homogeneous quasimorphisms.From now on we assume that all Lie algebras are real and finite-dimensional. We denote by Q(g) the space of Lie quasi-states on g and by Q(g) ⊂ Q(g) the subspace of continuous Lie quasi-states on g respectively. Note that the adjoint group associated to the Lie algebra g acts on these spaces by g.ζ(X ) = ζ(Ad(g) −1 (X )).

show abstract

Automatic continuity of pseudocharacters on semisimple Lie groups

Cited by 9 publications

References 22 publications

The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures

The action homomorphism, quasimorphisms and moment maps on the space of compatible almost complex structures

A version of van der Waerden's theorem and a proof of Mishchenko's conjecture on homomorphisms of locally compact groups

Quasi-state rigidity for finite-dimensional Lie algebras

Contact Info

Product

Resources

About