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151.
It is known that the orbit closures for the representations of the equioriented Dynkin quivers ?
n
are normal and Cohen–Macaulay varieties with rational singularities. In the paper we prove the same for the Dynkin quivers
?
n
with arbitrary orientation.
Received: 25 October 2000 / Revised version: 28 February 2001 相似文献
152.
P. J. Vassiliou 《Acta Appl Math》1987,8(2):107-147
We study coupled systems of nonlinear wave equations from the point of view of their formal Darboux integrability. By making use of Vessiot's geometric theory of differential equations, it is possible to associate to each system of nonlinear wave equations a module of vector fields on the second-order jet bundle — the Vessiot distribution. By imposing certain conditions of the structure of the Vessiot distributions, we identify the so-called separable Vessiot distributions. By expressing the separable Vessiot distributions in a basis of singular vector fields, we show that there are, at most, 27 equivalence classes of such distributions. Of these, 14 classes are associated with Darboux integrable nonlinear systems. We take one of these Darboux integrable classes and show that it is in correspondence with the class of six-dimensional simply transitive Lie algebras. Finally, this later result is used to reduce the problem of constructing exact general solutions of the nonlinear wave equations understudy to the integration of Lie systems. These systems were first discovered by Sophus Lie as the most general class of ordinary differential equations which admit nonlinear superposition principles. 相似文献
153.
The notion of a formally smooth bimodule is introduced and its basic properties are analyzed. In particular it is proven that a B-A bimodule M which is a generator left B-module is formally smooth if and only if the M-Hochschild dimension of B is at most one. It is also shown that modules M which are generators in the category σ[M] of M-subgenerated modules provide natural examples of formally smooth bimodules. 相似文献
154.
155.
A. K. Goyal 《Periodica Mathematica Hungarica》1986,17(1):13-20
In this paper,D-strong and almostD-strong near-rings have been defined. It has been proved that ifR is aD-strongS-near ring, then prime ideals, strictly prime ideals and completely prime ideals coincide. Also ifR is aD-strong near-ring with identity, then every maximal right ideal becomes a maximal ideal and moreover every 2-primitive near-ring becomes a near-field. Several properties, chain conditions and structure theorems have also been discussed.Most of the parts of this paper are included in author's doctoral dissertation at Sukhadia University Udaipur (1983). The author expresses his gratitude to Dr.S. C. Choudhary for his kind guidance. 相似文献
156.
We present a direct and rather elementary method for defining and analyzing one-dimensional Schrödinger operators H = −d2/dx2 + μ with measures as potentials. The basic idea is to let the (suitably interpreted) equation −f′′ + μ f = zf take center stage.We show that the basic results from direct and inverse spectral theory then carry over to Schrödinger operators with measures. 相似文献
157.
In the article, we study the structure of Galois coverings of self-injective artin algebras with infinite cyclic Galois groups. In particular, we characterize all basic, connected, self-injective artin algebras having Galois coverings by the repetitive algebras of basic connected artin algebras and with the Galois groups generated by positive automorphisms of the repetitive algebras. 相似文献
158.
We give the complete set of irreducible representations of U(SU(2))q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not highest-weight representations. 相似文献
159.
Jacques Helmstetter 《Advances in Applied Clifford Algebras》2008,18(2):153-196
A meson algebra is involved in the Duffin wave equation for mesons in the same way as a Clifford algebra is involved in the
Dirac wave equation for electrons. Therefore meson algebras too should have geometrical properties after the manner of Grassmann.
Actually it is possible to define interior multiplications with similar properties, and deformations too. Every meson algebra
is a deformation of a neutral meson algebra, in the same way as (almost) every Clifford algebra is a deformation of an exterior
algebra. Some applications follow: the PBW-property is proved for all meson algebras, the injectiveness of Jacobson’s diagonal
morphism is proved with the minimal hypothesis, and the existence of Lipschitz monoids is established at least for meson algebras
over fields.
相似文献
160.
Xinyun Zhu 《Linear algebra and its applications》2008,428(4):919-929
We show that under certain conditions, the N = 1 types A and D quivers are of finite representation type. 相似文献