Toda chains with type Am Lie algebra for multidimensional m-component perfect fluid cosmology
نویسنده
چکیده
We consider a D-dimensional cosmological model describing an evolution of Ricci-flat factor spaces, M1, . . . , Mn (n ≥ 3), in the presence of an m-component perfect fluid source (n− 1 ≥ m ≥ 2). We find characteristic vectors, related to the matter constants in the barotropic equations of state for fluid components of all factor spaces. We show that, in the case where we can interpret these vectors as the root vectors of a Lie algebra of Cartan type Am = sl(m + 1,C), the model reduces to the classical open m-body Toda chain. Using an elegant technique by Anderson [1] for solving this system, we integrate the Einstein equations for the model and present the metric in a Kasner-like form. PACS numbers: 04.20.J, 04.60.+n, 03.65.Ge
منابع مشابه
TODA CHAINS WITH TYPE Am LIE ALGEBRA FOR MULTIDIMENSIONAL CLASSICAL COSMOLOGY WITH INTERSECTING p-BRANES
We consider a D-dimensional cosmological model describing an evolution of (n+1) Einstein factor spaces (n ≥ 2) in the theory with several dilatonic scalar fields and generalized electro-magnetic forms, admitting an interpretation in terms of intersecting p-branes. The equations of motion of the model are reduced to the Euler-Lagrange equations for the so called pseudo-Euclidean Toda-like system...
متن کاملRUSSIAN GRAVITATIONAL ASSOCIATION CENTER FOR SURFACE AND VACUUM RESEARCH DEPARTMENT OF FUNDAMENTAL INTERACTIONS AND METROLOGY RGA-CSVR-009/94 gr-qc/9407019 MULTIDIMENSIONAL COSMOLOGY WITH MULTICOMPONENT PERFECT FLUID AND TODA LATTICES
The integration procedure for multidimensional cosmological models with multicomponent perfect fluid in spaces of constant curvature is developed. Reduction of pseudo-Euclidean Toda-like systems to the Euclidean ones is done. Some known solutions are singled out from those obtained. The existence of the wormholes is proved. PACS numbers: 04.20.J, 04.60.+n, 03.65.Ge
متن کاملDouble derivations of n-Lie algebras
After introducing double derivations of $n$-Lie algebra $L$ we describe the relationship between the algebra $mathcal D(L)$ of double derivations and the usual derivation Lie algebra $mathcal Der(L)$. In particular, we prove that the inner derivation algebra $ad(L)$ is an ideal of the double derivation algebra $mathcal D(L)$; we also show that if $L$ is a perfect $n$-Lie algebra wit...
متن کاملLoop Algebras, Gauge Invariants and a New Completely Integrable System
One fruitful motivating principle of much research on the family of integrable systems known as “Toda lattices” has been the heuristic assumption that the periodic Toda lattice in an affine Lie algebra is directly analogous to the nonperiodic Toda lattice in a finite-dimensional Lie algebra. This paper shows that the analogy is not perfect. A discrepancy arises because the natural generalizatio...
متن کاملOn Some Class of Multidimensional Nonlinear Integrable Systems A
On the base of Lie algebraic and differential geometry methods, a wide class of multidimensional nonlinear integrable systems is obtained, and the integration scheme for such equations is proposed. 1. In the report we give a Lie algebraic and differential geometry derivation of a wide class of nonlinear integrable systems of partial differential equations for the functions depending on an arbit...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997