Publications and Preprints
Luiz A. B. San Martin
Morse decomposition of semiflows
on fiber bundles
with Mauro Patrão
October, 2005
Semiflows on
topological spaces: Chain transitivity and shadowing semigroups
with Mauro Patrão
September, 2005
Lie algebras with complex structures having nilpotent eigenspaces
with Edson C. Licurgo dos Santos
August, 2995
Semigroups in
Symmetric Lie Groups
with com Laércio J. dos Santos
June, 2005
Invariant cones and convex sets for bilinear control
systems and parabolic
type of semigroups
with O. G. do Rocio e A. J. Santana
Journal of Dynamics and Control
Systems, to appear.
May, 2005
Control sets and total positivity
with V. Ayala e W. Kliemann
Semigroup Forum 69(1)
(2004), 113--140.
MR 2 063 983
Invariant nearly-Kähler
structures.
with Rita de Cássia Jesus Silva
September, 2003
Covering space for monotonic homotopy
of trajectories of control systems
with Fritz Colonius and Eyup Kizil
J. Diff. Equations, 216, issue 2 (2005),
324-353. MR 2 162 339
f-Structures on
the Classical Flag Manifold which
Admit (1,2)-Symplectic Metrics
with Nir Cohen, Caio J. C. Negreiros, Marlio Paredes e Sofia Pinzón
Tohoku Mathematical
Journal (2) 57 (2005), no. 2, 261--271. MR 2137470
Maximal chain transitive sets for local groups
with Carlos J. Braga Barros
Boletim da Sociedade Paranaense
de Matemática (3) 21 (2003), no 1-2, 113-125. MR 2 066 951
Geometric properties of invariant connections on Sl(n,R)/SO(n)
with Marco A. N. Fernandes
Journal of Geometry
and Physics, Volume 47, Issues 2-3 (2003), 369-377. MR 1 991 481
Chain transitive sets for flows on flag bundles (pdf zip)
with Carlos J.
This paper applies the theory of semigroups in semi-simple Lie groups to a problem in dynamical
systems a
-July, 2002. To appear in Forum Mathematicum
http://www.degruyter.de/rs/278_3128_DEU_h.htm
Connected components of open semigroups
in semi-simple Lie groups (ps zip)
with Osvaldo Germano do Rocio
-March, 2002.
A rank-three condition for invariant (1,2)-symplectic almost Hermitian structures on flag manifolds (dvi)
with Nir Cohen and Caio J. C. Negreiros
-September, 2001. To appear
in Boletim da Sociedade Brasileira de Matemática (Bulletin of the Brazilian Math. Soc.).
Invariant almost Hermitian
structures on flag manifolds
with Caio J. C. Negreiros
Given a complex semi-simple Lie group G its
'Fundamental homogeneous space' (maximal flag manifold) is the coset B = G/P modulo a Borel
subgroup P of G. There exists an extensive literature about G/P for several
reasons which range from questions in Differential Geometry to Representation
Theory. In the context of compact Lie groups the spaces G/P are the given by cosets U/T where U is a compact real form of G and T is a
maximal torus of U. These spaces are also known
generically as 'flag manifolds' (or maximal flag manifolds), since G/P
identifies with concrete space of (complete) flags of subspaces of an
n-dimensional complex vector space when G is the special linear group Sl(n,C).
This paper studies U-invariant almost complex
geometry on B = G/P. A basic issue are the invariant (1,2)-symplectic almost Hermitian
structures. Two characterizations of these structures are given: 1) by means of
the abelian ideals of a Borel subalgebra and 2) in
terms of the alcoves of the corresponding affine Weyl
group. The first characterization generalizes the results of the paper below,
with independent proofs. In fact, instead of tournaments, that are linked only
to the Sl(n,C) (concrete) flag manifolds, we use directly the algebra
(combinatorics) of root systems, which gives life to
the theory of semi-simple Lie algebras.
Having at hand the characterization of (1,2)-symplectic structures we give
a classification of the invariant almost Hermitian
structures into four classes.
Advances in Mathematics, 178 (2003), 277-310. (ps zip)
(1,2)-Symplectic
metrics on flag manifolds and trournaments (dvi)
with Nir Cohen and Caio J. C. Negreiros
This paper is devoted to a problem in complex
geometry, namely the characterization of almost complex structures on manifolds
which admit Riemannian metrics which are (1,2)-symplectic (or as they are also called almost Kahler metrics). Here the combinatorics
of tournaments is used to characterize those invariant almost complex
structures in the complex full flag manifold which admit an invariant (1,2)-symplectic metrics.
Bulletin of
The homotopy type of Lie semigroups in semi-simple Lie groups
with Alexandre J. Santana
A noncompact
semi-simple Lie group G decomposes as the product of its corresponding
symmetric space by the maximal compact subgroup K. This decompositions
entails that the topology of G lives in K. In this paper its proved something
similar holds for a semigroup S contained in G.
Namely there is a compact subgroup K(S) of K giving the topology of S, in the
sense that S and K(S) are homotopy equivalent
(actually a stronger statement holds: A coset of K(S)
is a deformation retract of the interior of S. These results are proved with
the assumption that S is generated by a cone in the Lie algebra of G (since it
is not assumed that S is closed this condition is a slight extension of the
concept of Lie semigroup). Actually the proofs hold
for semigroups having large subsemigroups
generated by cones in Lie algebra. For instance, the semigroup
of positive matrices is not generated by a cone in the Lie algebra but it
contains a large such semigroup sothat
the homotopy type of the semigroup
of nxn positive matrices can be computed by the
methods of this paper (it is the homotopy type of the
orthogonal group SO(n-1).
Monattshefte für Mathematik, 136 (2002),
151-173. (ps zip)
Nonexistence of invariant semigroups
in affine symmetric spaces
The semigroups that
usually appear in the theory of causal symmetric spaces are infinitesimally
generated by invariant cones. These cones occur only when the affine pair are of Hermitian type, so that
infinitesimally generated invariant semigroups do not
exist except in this case. This paper drops the term 'infinitesimally
generated' from that statement: There exists an invariant semigroup
with nonempty interior only if the affine symmetric space is of Hermitian type. This result was conjectured before by
Joachim Hilgert and Karl-Hermann Neeb
(Compression semigroups of open orbits on real flag
manifolds. Monatsh. Math.,119, (1995), 187-214.)
Mathematische Annalen,
321, (2001), 587-600.
A family of maximal noncontrollable
Lie wedges with empty interior
A natural question in Lie semigroup
theory is whether the maximal Lie wedges in a Lie
algebra are generating cones, i.e, have nonempty
interior in the Lie algebra. This is true for solvable Lie algebras. Recently
Dirk Mittenhuber built maximal Lie wedges in the rank
one su(1,n).
This paper gives other examples of such Lie wedges: The Lie wedge of the semigroup of dxd matrices having
positive k-minors is maximal and have empty interior if d and k are even.
Systems & Control Letters (Special Issue on
Lie Theory and Applications to Control) 43 (1) (2001) pp. 53-57.
Maximal semigroups in
semi-simple Lie groups (dvi)
The maximal semigroups
with nonempty interior in a semi-simple Lie group with finite center are
characterized. They are compression semigroups of
specific type of sets, the B-convex sets.
Transactions of American Mathematical Ssociety, 353 (2001), 5165-5184.
Fisher Information and alfa-connections
for a class of Transformational models
with Marco A. N. Fernandes
We characterize the invariant alfa-connections for statistical transformational models
parameterized by homogeneous spaces. It turns out that in the semi-simple
setting only the A_l series admit nontrivial
invariant connections. Some properties of these connections are derived.
Differential Geometry and its Applications , 12 (2000), 165-184.
Lyapunov
Exponents for Stochastic Differential Equations in Semi-simple Lie groups (dvi)
with Paulo R. C. Ruffino
We write an integral formula for the asymptotics of the A-part in the Iwasawa
decomposition of the solution of an invariant stochastic equation in a
semi-simple group. The integral is with respect to the invariant measure on the
maximal flag manifold, the Furstenberg boundary. The integrand of the formula
is related to the Takeuchi-Kobayashi Riemannian metric in the flag manifold -
January/1998. To appear in Archivum
Mathematicum.
Controllability of Discrete-time Control Systems on
the Symplectic Group
with Carlos J. Braga Barros.
Gives sufficient conditions for the
controllability of a 'bilinear' discrete-time control system when the system
evolves in the symplectic group. It is similar in spirit and
techniques to "On global controllability ..." (see below)
Systems & Control Letters, 42 (2001),
95-100. (ps zip)
Orders and Domains of Attraction of Control Sets in
Flag Manifolds
Relates the Bruhat-Chevalley
order in the Weyl group with the order of the control
sets in the flag manifolds. Journal of Lie Theory (JoLT) ,
8, (1998), 335-350. (ps
zip)
Homogeneous Spaces Admitting Transitive Semigroups
The transitivity in a homogeneous space of a
proper semigroup of a semi-simple Lie group is a rare
event. Journal of Lie Theory (JoLT) ,
vol. 8 (1998), 111-128. (ps
zip)
Transitive Actions of Semigroups
in Semi-simple Lie Groups
with Pedro A. Tonelli.
Necessary conditions for an action
of a semigroup to be transitive on a homogeneous
space. Semigroup Forum, 58 (1999), 142-151.
On the Action of a Semigroup
in a Fiber Bundle (dvi)
with Carlos J. Braga Barros.
Studies control sets for semigroups
acting in a fiber bundle in a topological setting. The invariant control sets
are described by invariant control sets in the base space and in the fibers. Matematica Contemporanea, 13
(1997), 1-19.
On Global Controllability of Discrete-Time Control
Systems
Gives sufficient conditions in order
that a discrete-time bilinear control system is controllable. The conditions are given in terms
of the coefficients of the system and are similar to the conditions of Jurdjevic and Kupka in the
continuous-time. Mathematics of Control, Signals, and Systems (MCSS) vol. 8 (1995) 279-297. (ps zip)
Controllability of two-dimensional bilinear systems:
restricted controls and discrete-time.
with V. Ayala.
Provides necessary and sufficient
algebraic conditions for the controllability of a bilinear system in dimension
two. The
approach is through Lie theory with the systems divided according to the
transitive groups they generate. Proyecciones, vol.
18, 2 (1999), 207-223. MR 1 727 729. (ps zip)
Controllability of Two-Dimensional Bilinear Systems (dvi)
with Carlos J. Braga Barros, João R. Gonçalves Filho and Osvaldo G. do Rocio.
Provides necessary and sufficient
algebraic conditions for the controllability of a bilinear system in dimension
two. The
approach is through Lie theory with the systems divided according to the
transitive groups they generate. Proyecciones Revista de Matematica
vol. 15 (1996), 111-139. (ps
zip)
Chain Control Sets for Semigroup
Actions
with Carlos J. Braga Barros.
Generalizes to general semigroup actions the concept of chain control set relating
it to control sets for perturbed semigroups. Chain control sets for semigroups in flag manifolds are characterized. Computational and Applied
Mathematics vol. 15
(1996), 257-276. (ps
zip)
Semigroup
Actions on Homogeneous Spaces
with Pedro A. Tonelli.
Builds a theory of semigroups in semi-simple Lie groups with finite center
from the action on the flag manifolds of the group. Semigroup Forum vol. 50 (1995), 59-88. (ps zip)
On the number of control sets in projective spaces
with Carlos J. Braga Barros.
Counts the number of control sets of a linear semigroup acting in the
projective space. Systems & Control Letters vol. 29 (1996), 21-26.
Discrete Semigroups in
Nilpotent Groups
with Osvaldo G. do Rocio.
Shows that a proper semigroup in a lattice of a nilpotent group is contained in
proper semigroup with interior points. In particular the maximal semigroups of a lattice are intersections of maximal semigroups with nonvoid interior
with the lattice. Semigroup Forum vol. 51 (1995), 125-133.
Semigroups in
Lattices of Solvable Groups
with Osvaldo G. do Rocio.
Generalizes the previous paper to solvable groups. The results here are not plain. They require an assumption about the immaginary roots of the adjoint representation of the Lie algebra of the group. Journal of Lie Theory (JOLT) (1995) 188-202.
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Last modified November 2005