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961.
962.
文献[1]从Euclid空间R^v(v≥1)的一个半格S出发,定义了一个Jordan代数J(S):然后通过Tits—Kantor-Koecher方法由J(S)构造出Lie代数G(J(S)).最后利用G(J(S))得到A1型扩张仿射Lie代数L(J(S)).本文给出v=2,S为格时。A1型扩张仿射Lie代数L(J(S))的Z^2一分次自同构群. 相似文献
963.
Huan-he Dong xinzeng wang 《Communications in Nonlinear Science & Numerical Simulation》2009,14(12):4071-4077
Lie algebras and Lie super algebra are constructed and integrable couplings of NLS–MKdV hierarchy are obtained. Furthermore, its Hamiltonian and Super-Hamiltonian are presented by using of quadric-form identity and super-trace identity. The method can be used to produce the Hamiltonian structures of the other integrable and super-integrable systems. 相似文献
964.
We study the behavior of the Etingof–Kazhdan quantization functors under the natural duality operations of Lie bialgebras
and Hopf algebras. In particular, we prove that these functors are “compatible with duality”, i.e., they commute with the
operation of duality followed by replacing the coproduct by its opposite. We then show that any quantization functor with
this property also commutes with the operation of taking doubles. As an application, we show that the Etingof–Kazhdan quantizations
of some affine Lie superalgebras coincide with their Drinfeld–Jimbo-type quantizations.
To the memory of Paulette Libermann (1919–2007) 相似文献
965.
V. A. Kyrov 《Russian Mathematics (Iz VUZ)》2009,53(7):7-16
In this paper we define a phenomenologically symmetric local Lie group of transformations of an arbitrary-dimensional space. We take as a basis the axiom scheme of the theory of physical structures. Phenomenologically symmetric groups of transformations are nondegenerate both with respect to coordinates and to parameters. We obtain a multipoint invariant of this group of transformations and relate it with Ward quasigroups. We define a substructure of a physical structure as a certain phenomenologically symmetric subgroup of transformations. We establish a criterion for the phenomenological symmetry of the Lie group of transformations and prove the uniqueness of a structure with the minimal rank. We also introduce the notion of a phenomenologically symmetric product of physical structures. 相似文献
966.
Suppose R is an idempotence-diagonalizable ring. Let n and m be two arbitrary positive integers with n ≥ 3. We denote by Mn(R) the ring of all n x n matrices over R. Let (Jn(R)) be the additive subgroup of Mn(R) generated additively by all idempotent matrices. Let JJ = (Jn(R)) or Mn(R). We describe the additive preservers of idempotence from JJ to Mm(R) when 2 is a unit of R. Thereby, we also characterize the Jordan (respectively, ring and ring anti-) homomorphisms from Mn (R) to Mm (R) when 2 is a unit of R. 相似文献
967.
968.
969.
Yuming Liu 《Proceedings of the American Mathematical Society》2006,134(6):1605-1613
Let and be two Artin algebras with no semisimple summands. Suppose that there is a stable equivalence between and such that is induced by exact functors. We present a nice correspondence between indecomposable modules over and . As a consequence, we have the following: (1) If is a self-injective algebra, then so is ; (2) If and are finite dimensional algebras over an algebraically closed field , and if is of finite representation type such that the Auslander-Reiten quiver of has no oriented cycles, then and are Morita equivalent.
970.
For a complex semisimple Lie group and a real form we define a Poisson structure on the variety of Borel subgroups of with the property that all -orbits in as well as all Bruhat cells (for a suitable choice of a Borel subgroup of ) are Poisson submanifolds. In particular, we show that every non-empty intersection of a -orbit and a Bruhat cell is a regular Poisson manifold, and we compute the dimension of its symplectic leaves.