共查询到8条相似文献,搜索用时 62 毫秒
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Meighan I. Dillon 《代数通讯》2017,45(8):3515-3530
The ?-grading determined by a long simple root of a rank n+1 a?ne Lie algebra over ? arises from a representation of a rank n semi-simple complex Lie algebra. Analysis of the relationship between the grading and the representation yields constructions that generalize the minuscule and adjoint algorithms as well as Kac’s construction of nontwisted a?ne Lie algebras. 相似文献
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Abbas Nasrollah Nejad 《代数通讯》2018,46(8):3553-3562
The Alu? algebra is an algebraic definition of a characteristic cycle of a hypersurface in intersection theory. In this paper, we study the Alu? algebra of quasi-homogeneous and locally Eulerian hypersurfaces with only isolated singularities. We prove that the Jacobian ideal of an a?ne hypersurface with isolated singularities is of linear type if and only if it is locally Eulerian. We show that the gradient ideal of a projective hypersurface with only isolated singularities is of linear type if and only if the a?ne curve in each a?ne chart associated to singular points is locally Eulerian. We show that the gradient ideal of Nodal and Cuspidal projective plane curves are of linear type. 相似文献
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Yuly Billig 《代数通讯》2018,46(8):3413-3429
We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible a?ne variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth a?ne variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered. 相似文献
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The quadratic sum-of-ratios fractional program problem has a broad range of applications in practical problems. This article will present an e?cient branch-and-bound algorithm for globally solving the quadratic sum-of-ratios fractional program problem. In this algorithm, lower bounds are computed by solving a series of parametric relaxation linear programming problems, which are established by utilizing new parametric linearizing technique. To enhance the computational speed of the proposed algorithm, a rectangle reducing tactic is used to reject a part of the investigated rectangle or the whole rectangle where there does not contain any global optimal solution of the quadratic sum-of-ratios fractional program problem. Compared with the known approaches, the proposed algorithm does not need to introduce new variables and constraints. Therefore, the proposed algorithm is more suitable for application in engineering. 相似文献
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Goran Trupčević 《代数通讯》2018,46(8):3663-3673
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After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coe?cients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coe?cients of the center of a finite group algebra in terms of irreducible characters. 相似文献