290 research outputs found
Non-solvable contractions of semisimple Lie algebras in low dimension
The problem of non-solvable contractions of Lie algebras is analyzed. By
means of a stability theorem, the problem is shown to be deeply related to the
embeddings among semisimple Lie algebras and the resulting branching rules for
representations. With this procedure, we determine all deformations of
indecomposable Lie algebras having a nontrivial Levi decomposition onto
semisimple Lie algebras of dimension , and obtain the non-solvable
contractions of the latter class of algebras.Comment: 21 pages. 2 Tables, 2 figure
Vlasov moment flows and geodesics on the Jacobi group
By using the moment algebra of the Vlasov kinetic equation, we characterize
the integrable Bloch-Iserles system on symmetric matrices
(arXiv:math-ph/0512093) as a geodesic flow on the Jacobi group. We analyze the
corresponding Lie-Poisson structure by presenting a momentum map, which both
untangles the bracket structure and produces particle-type solutions that are
inherited from the Vlasov-like interpretation. Moreover, we show how the Vlasov
moments associated to Bloch-Iserles dynamics correspond to particular subgroup
inclusions into a group central extension (first discovered in
arXiv:math/0410100), which in turn underlies Vlasov kinetic theory. In the most
general case of Bloch-Iserles dynamics, a generalization of the Jacobi group
also emerges naturally.Comment: 45 page
Poisson structures for reduced non-holonomic systems
Borisov, Mamaev and Kilin have recently found certain Poisson structures with
respect to which the reduced and rescaled systems of certain non-holonomic
problems, involving rolling bodies without slipping, become Hamiltonian, the
Hamiltonian function being the reduced energy. We study further the algebraic
origin of these Poisson structures, showing that they are of rank two and
therefore the mentioned rescaling is not necessary. We show that they are
determined, up to a non-vanishing factor function, by the existence of a system
of first-order differential equations providing two integrals of motion. We
generalize the form of that Poisson structures and extend their domain of
definition. We apply the theory to the rolling disk, the Routh's sphere, the
ball rolling on a surface of revolution, and its special case of a ball rolling
inside a cylinder.Comment: 22 page
Manin products, Koszul duality, Loday algebras and Deligne conjecture
In this article we give a conceptual definition of Manin products in any
category endowed with two coherent monoidal products. This construction can be
applied to associative algebras, non-symmetric operads, operads, colored
operads, and properads presented by generators and relations. These two
products, called black and white, are dual to each other under Koszul duality
functor. We study their properties and compute several examples of black and
white products for operads. These products allow us to define natural
operations on the chain complex defining cohomology theories. With these
operations, we are able to prove that Deligne's conjecture holds for a general
class of operads and is not specific to the case of associative algebras.
Finally, we prove generalized versions of a few conjectures raised by M. Aguiar
and J.-L. Loday related to the Koszul property of operads defined by black
products. These operads provide infinitely many examples for this generalized
Deligne's conjecture.Comment: Final version, a few references adde
Fact or Factitious? A Psychobiological Study of Authentic and Simulated Dissociative Identity States
BACKGROUND: Dissociative identity disorder (DID) is a disputed psychiatric disorder. Research findings and clinical observations suggest that DID involves an authentic mental disorder related to factors such as traumatization and disrupted attachment. A competing view indicates that DID is due to fantasy proneness, suggestibility, suggestion, and role-playing. Here we examine whether dissociative identity state-dependent psychobiological features in DID can be induced in high or low fantasy prone individuals by instructed and motivated role-playing, and suggestion. METHODOLOGY/PRINCIPAL FINDINGS: DID patients, high fantasy prone and low fantasy prone controls were studied in two different types of identity states (neutral and trauma-related) in an autobiographical memory script-driven (neutral or trauma-related) imagery paradigm. The controls were instructed to enact the two DID identity states. Twenty-nine subjects participated in the study: 11 patients with DID, 10 high fantasy prone DID simulating controls, and 8 low fantasy prone DID simulating controls. Autonomic and subjective reactions were obtained. Differences in psychophysiological and neural activation patterns were found between the DID patients and both high and low fantasy prone controls. That is, the identity states in DID were not convincingly enacted by DID simulating controls. Thus, important differences regarding regional cerebral bloodflow and psychophysiological responses for different types of identity states in patients with DID were upheld after controlling for DID simulation. CONCLUSIONS/SIGNIFICANCE: The findings are at odds with the idea that differences among different types of dissociative identity states in DID can be explained by high fantasy proneness, motivated role-enactment, and suggestion. They indicate that DID does not have a sociocultural (e.g., iatrogenic) origin
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Classical and Quantum Systems: Alternative Hamiltonian Descriptions
In complete analogy with the classical situation (which is briefly reviewed)
it is possible to define bi-Hamiltonian descriptions for Quantum systems. We
also analyze compatible Hermitian structures in full analogy with compatible
Poisson structures.Comment: To appear on Theor. Math. Phy
The graded Jacobi algebras and (co)homology
Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in
the context of graded Jacobi brackets on graded commutative algebras. This
unifies varios concepts of graded Lie structures in geometry and physics. A
method of describing such structures by classical Lie algebroids via certain
gauging (in the spirit of E.Witten's gauging of exterior derivative) is
developed. One constructs a corresponding Cartan differential calculus (graded
commutative one) in a natural manner. This, in turn, gives canonical generating
operators for triangular Jacobi algebroids. One gets, in particular, the
Lichnerowicz-Jacobi homology operators associated with classical Jacobi
structures. Courant-Jacobi brackets are obtained in a similar way and use to
define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi
structure. All this offers a new flavour in understanding the
Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J.
Phys. A: Math. Ge
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