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Let V be a 6-dimensional vector space over a field F, let f be a nondegenerate alternating bilinear form on V and let Sp(V,f)≅Sp6(F) denote the symplectic group associated with (V,f). The group GL(V) has a natural action on the third exterior power ?3V of V and this action defines five families of nonzero trivectors of V (four of whose are orbits for any choice of F). In this paper, we divide three of these five families into orbits for the action of Sp(V,f)⊆GL(V) on ?3V. 相似文献
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Dragomir Ž. Djoković 《Linear and Multilinear Algebra》2013,61(1):3-39
Let U?V denote the tensor product of two finite dimensional vector spaces U and V over an infinite field. Let k be a positive integer such that kdim U and k dim V Let Dk denote the set of all non-zero elements of U?V of rank less than k. In this paper we study linear transformations T on U?V such that (TDk )?Dk . 相似文献
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Hui Li 《Transactions of the American Mathematical Society》2005,357(3):983-998
Let be a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian action such that the fixed point set consists of isolated points or surfaces. Assume dim . In an earlier paper, we defined a certain invariant of such spaces which consists of fixed point data and twist type, and we divided the possible values of these invariants into six ``types'. In this paper, we construct such manifolds with these ``types'. As a consequence, we have a precise list of the values of these invariants.
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T. Kappeler F. Serier P. Topalov 《Proceedings of the American Mathematical Society》2008,136(5):1691-1698
We prove that the Birkhoff map for KdV constructed on can be interpolated between and . In particular, the symplectic phase space can be described in terms of Birkhoff coordinates.
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Hui Li 《Transactions of the American Mathematical Society》2003,355(11):4543-4568
Assume is a connected, compact 6-dimensional symplectic manifold equipped with a semi-free Hamiltonian circle action, such that the fixed point set consists of isolated points or compact orientable surfaces. We restrict attention to the case . We give a complete list of the possible manifolds, and determine their equivariant cohomology rings and equivariant Chern classes. Some of these manifolds are classified up to diffeomorphism. We also show the existence for a few cases.
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Mihai Halic 《manuscripta mathematica》1999,99(3):371-381
The article investigates the geography of closed, connected and simply connected, six-dimensional manifolds. It is proved
that any triple of integers satisfying some necessary arithmetical restrictions occurs as the Chern triple of such a manifold.
The main tools used for producing the examples are the symplectic connected sum and the symplectic blow-up.
Received: 28 May 1998 / Revised version: 22 January 1999 相似文献
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A. Shmeljov 《Journal of Mathematical Sciences》1996,82(5):3707-3712
Translated from Itogi Nauki i Tekhniki, Seriya Sovremenaya Matematika i Ee Prilozheniya. Tematicheskie Obzory. Vol. 20, Topologia-3,
1994. 相似文献
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Theoretical and Mathematical Physics - We study automorphisms of a $$6$$ -torus with one-dimensional stable and unstable manifolds, and a four-dimensional center manifold. Such automorphisms are... 相似文献
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In continuation of our earlier work [2] we describe the indecomposable representations and the Auslander-Reiten quivers of
a family of vector space categories playing an important role in the study of domestic finite dimensional algebras over an
algebraically closed field. The main results of the paper are applied in our paper [3] where we exhibit a wide class of almost
sincere domestic simply connected algebras of arbitrary large finite global dimensions and describe their Auslander-Reiten
quivers. 相似文献
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Manuel Valdivia 《manuscripta mathematica》1974,14(3):241-247
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Wolfgang Krieger 《Probability Theory and Related Fields》1969,11(2):98-119
Summary This paper continues the investigations of On Non-Singular Transformations of a Measure Space I. 相似文献
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