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991.
Nguyen H. V. Hu'ng Tran Ngoc Nam 《Transactions of the American Mathematical Society》2001,353(12):5029-5040
Let the mod 2 Steenrod algebra, , and the general linear group, , act on with in the usual manner. We prove the conjecture of the first-named author in Spherical classes and the algebraic transfer, (Trans. Amer. Math Soc. 349 (1997), 3893-3910) stating that every element of positive degree in the Dickson algebra is -decomposable in for arbitrary 2$">. This conjecture was shown to be equivalent to a weak algebraic version of the classical conjecture on spherical classes, which states that the only spherical classes in are the elements of Hopf invariant one and those of Kervaire invariant one.
992.
BRST resolution is studied for the principally graded Wakimoto module of
recently found in math.QA/0005203. The submodule structure is completely determined and irreducible representations can be obtained as the zero-th cohomology group. 相似文献
993.
994.
Under certain constraints on the characteristic of a field , the commutative standard enveloping q-algebra >B of a commutative triple system A over is defined. It is proved that(1) if the algebra B is simple, then the system A is simple;(2) if the system A is simple, then B either is simple or decomposes into the direct sum of two isomorphic simple subalgebras (as of ideals). 相似文献
995.
Let A be a finite-dimensional algebra over a field k. The derived Picard group DPic
k
(A) is the group of triangle auto-equivalences of D>
b( mod A) induced by two-sided tilting complexes. We study the group DPic
k
(A) when A is hereditary and k is algebraically closed. We obtain general results on the structure of DPic
k
, as well as explicit calculations for many cases, including all finite and tame representation types. Our method is to construct a representation of DPic
k
(A) on a certain infinite quiver irr. This representation is faithful when the quiver of A is a tree, and then DPic
k
(A) is discrete. Otherwise a connected linear algebraic group can occur as a factor of DPic
k
(A). When A is hereditary, DPic
k
(A) coincides with the full group of k-linear triangle auto-equivalences of Db( mod A). Hence, we can calculate the group of such auto-equivalences for any triangulated category D equivalent to Db( mod A. These include the derived categories of piecewise hereditary algebras, and of certain noncommutative spaces introduced by Kontsevich and Rosenberg. 相似文献
996.
A DC-space (or space of dense constancies) is a Tychonoff space X such that for each f C(X) there is a family of open sets {U
i
: i I}, the union of which is dense in X, such that f, restricted to each U
i
, is constant. A number of characterizations of DC-spaces are given, which lead to an algebraic generalization of the concept, which, in turn, permits analysis of DC-spaces in the language of archimedean f-algebras. One is led naturally to the notion of an almost DC-space (in which the densely constant functions are dense), and it is shown that all metrizable spaces have this property. 相似文献
997.
A. A. Pavlov 《Acta Appl Math》2001,68(1-3):137-157
We define N-theory as being an analogue of K-theory on the category of von Neumann algebras such that K
0(A)N
0(A) for any von Neumann algebra A. Moreover, it turns out to be possible to construct the extension of the Chern character to some homomorphism from N
0(A) to an even Banach cyclic homology of A. Also, we define generalized Lefschetz numbers for an arbitrary unitary endomorphism U of an A-elliptic complex. We study them in the situation when U is an element of a representation of some compact Lie group. 相似文献
998.
1. PreliminaryIt is well known that{1] a 8ymPlectic form is invariant along the trajectory of a Hamilto-nian system. Based on this fundamental property, certain techniques have been developed.The purpose of this paper is to extend such an approach to a wider class of dynamic systeIns,namely, genera1ized Hamiltonian systems. Our purpose is to investigate a class of dynaInicsystems, which possess a certain "geometric structure".Deflnition 1.1[1'2]. Let M be a tIlallifo1d. w E fl'(M) is call… 相似文献
999.
We calculate the dimensions of the second homology groups with trivial coefficients of nilpotent subalgebras of the Lie superalgebra
, which is the natural superanalog of the Witt algebra. The proof is based on direct calculations of the rank of the differential. As an application, we find deformations of the maximal nilpotent subalgebra in
. 相似文献
1000.