Publications (21)
Actions of semisimple Lie groups on circle bundles
Dave Witte, Robert J. Zimmer
Suppose G is a connected, simple, real Lie group with real rank at least two, M is an ergodic G-space with invariant probability measure, and f is a Homeo(T)-valued Borel cocycle,…
Automorphism groups with cyclic commutator subgroup and Hamilton cycles
Edward Dobson, Heather Gavlas, Joy Morris +1
It has been shown that there is a Hamilton cycle in every connected Cayley graph on each group G whose commutator subgroup is cyclic of prime-power order. This paper considers conn…
Archimedean superrigidity of solvable S-arithmetic groups
Dave Witte
Let $\Ga$ be a connected, solvable linear algebraic group over a number field~, let be a finite set of places of~ that contains all the infinite places, and let $\theints…
Transitive permutation groups of prime-squared degree
Edward Dobson, Dave Witte
We explicitly determine all of the transitive groups of degree p-squared, p a prime, whose Sylow p-subgroup is not the wreath product of two cyclic groups of order p. Furthermore,…
Cocycle superrigidity for ergodic actions of non-semisimple Lie groups
Dave Witte
Suppose is a semisimple Levi subgroup of a connected Lie group~, is a Borel -space with finite invariant measure, and $α\colon X \times G \to \GL_n(\real)$ is a Bore…
Prehomogeneous vector spaces and ergodic theory II
Akihiko Yukie, Roger Zierau, Dave Witte
We apply M. Ratner's theorem on closures of unipotent orbits to the study of three families of prehomogeneous vector spaces. As a result, we prove analogues of the Oppenheim Conjec…
On automorphisms of arithmetic subgroups of unipotent groups in positive characteristic
Lucy Lifschitz, Dave Witte
Let F be a local field of positive characteristic, and let G be either a Heisenberg group over F, or a certain (nonabelian) two-dimensional unipotent group over F. If H is an arith…
Homogeneous Lorentz manifolds with simple isometry group
Dave Witte
Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2,n), with n > 2, then the identity compone…
Correction to "Zero-entropy affine maps on homogeneous spaces
Dave Witte
Proposition~6.4 of the author's paper {\origpaper} is incorrect. This invalid proposition was used in the proof of Corollary~6.5, so we provide a new proof of the latter result.
Superrigid subgroups and syndetic hulls in solvable Lie groups
Dave Witte
This is an expository paper. It is not difficult to see that every group homomorphism from the additive group Z of integers to the additive group R of real numbers extends to a hom…
Hamiltonian Paths in Cartesian Powers of Directed Cycles
David Austin, Heather Gavlas, Dave Witte
The vertex set of the kth cartesian power of a directed cycle of length m can be naturally identified with the set of k-tuples of integers modulo m. For any two vertices v and w of…
Foliation-preserving Maps Between Solvmanifolds
Holly Bernstein, Dave Witte
For i = 1,2, let Gamma_i be a lattice in a simply connected, solvable Lie group G_i, and let X_i be a connected Lie subgroup of G_i. The double cosets Gamma_igX_i provide a foliati…
Real representations of semisimple Lie algebras have Q-forms
Dave Witte
We prove that each real semisimple Lie algebra G has a Q-form, such that every real representation of G can be realized over the rational numbers Q. This was previously proved by M…
Compact Clifford-Klein forms of homogeneous spaces of SO(2,n)
Hee Oh, Dave Witte
A homogeneous space G/H is said to have a compact Clifford-Klein form if there exists a discrete subgroup D of G that acts properly discontinuously on G/H, such that the quotient s…
Groups that do not act by automorphisms of codimension-one foliations
Renato Feres, Dave Witte
Let G be a finitely generated group having the property that any action of any finite-index subgroup of G by homeomorphisms of the circle must have a finite orbit. (By a theorem of…
Superrigid subgroups of solvable Lie groups
Dave Witte
Let be a discrete subgroup of a simply connected, solvable Lie group~, such that $\Ad_GÎ$ has the same Zariski closure as $\Ad G$. If $α\colon Î\to \GL_n(\real)$ is any…
Correction to "Measurable quotients of unipotent translations on homogeneous spaces
Dave Witte
The statements of Main~Theorem~1.1 and Theorem~2.1 of the author's paper [\emph{Trans.\ Amer.\ Math.\ Soc.}\ {\bf 345} (1994) 577--594] should assume that ~is discrete and ~…
Cartan-decomposition subgroups of SO(2,n)
Hee Oh, Dave Witte
For G = SL(3,R) and G = SO(2,n), we give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G has the property that there exists a compa…
Ergodic actions of semisimple Lie groups on compact principal bundles
Dave Witte, Robert J. Zimmer
Let G = SL(n,R) (or, more generally, let G be a connected, noncompact, simple Lie group). For any compact Lie group K, it is easy to find a compact manifold M, such that there is a…
Tessellations of homogeneous spaces of classical groups of real rank two
Alessandra Iozzi, Dave Witte
Let H be a closed, connected subgroup of a connected, simple Lie group G with finite center. The homogeneous space G/H has a "tessellation" if there is a discrete subgroup D of G,…
Cartan-decomposition subgroups of SU(2,n)
Alessandra Iozzi, Dave Witte
We give explicit, practical conditions that determine whether or not a closed, connected subgroup H of G = SU(2,n) has the property that there exists a compact subset C of G with C…