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991.
《Journal of Pure and Applied Algebra》2003,177(1):71-78
We prove that a Jordan superalgebra J containing the 10-dimensional exceptional Kac superalgebra K10 is isomorphic to (K10⊗FS)⊕J′, where S is an associative commutative algebra. 相似文献
992.
Xiaoping Xu 《Journal of Pure and Applied Algebra》2008,212(6):1253-1309
We construct irreducible modules of centrally-extended classical Lie algebras over left ideals of the algebra of differential operators on the circle, through certain irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries. The structures of vertex algebras associated with the vacuum representations of these algebras are determined. Moreover, we prove that under certain conditions, the highest-weight irreducible modules of centrally-extended classical Lie algebras of infinite matrices with finite number of nonzero entries naturally give rise to the irreducible modules of the simple quotients of these vertex algebras. From vertex algebra and its representation point of view, our results with positive integral central charge are high-order differential operator analogues of the well-known WZW models in conformal field theory associated with affine Kac-Moody algebras. Indeed, when the left ideals are the algebra of differential operators, our Lie algebras do contain affine Kac-Moody algebras as subalgebras and our results restricted on them are exactly the representation contents in WZW models. Similar results with negative central charge are also obtained. 相似文献
993.
We will deal with finitely additive measures on integers extending the asymptotic density. We will study their relation to the Lévy group G of permutations of N. Using a new characterization of the Lévy group G we will prove that a finitely additive measure extends density if and only if it is G-invariant. 相似文献
994.
A finite group action on a lens space L(p,q) has ‘type OR’ if it reverses orientation and has an invariant Heegaard torus whose sides are interchanged by the orientation-reversing elements. In this paper we enumerate the actions of type OR up to equivalence. This leads to a complete classification of geometric finite group actions on amphicheiral lens spaces L(p,q) with p>2. The family of actions of type OR is partially ordered by lifting actions via covering maps. We show that each connected component of this poset may be described in terms of a subset of the lattice of Gaussian integers ordered by divisibility. This results in a correspondence equating equivalence classes of actions of type OR with pairs of Gaussian integers. 相似文献
995.
Hamid Usefi 《Journal of Pure and Applied Algebra》2008,212(10):2182-2189
Let G be a group, S a subgroup of G, and F a field of characteristic p. We denote the augmentation ideal of the group algebra FG by ω(G). The Zassenhaus-Jennings-Lazard series of G is defined by Dn(G)=G∩(1+ωn(G)). We give a constructive proof of a theorem of Quillen stating that the graded algebra associated with FG is isomorphic as an algebra to the enveloping algebra of the restricted Lie algebra associated with the Dn(G). We then extend a theorem of Jennings that provides a basis for the quotient ωn(G)/ωn+1(G) in terms of a basis of the restricted Lie algebra associated with the Dn(G). We shall use these theorems to prove the main results of this paper. For G a finite p-group and n a positive integer, we prove that G∩(1+ω(G)ωn(S))=Dn+1(S) and G∩(1+ω2(G)ωn(S))=Dn+2(S)Dn+1(S∩D2(G)). The analogous results for integral group rings of free groups have been previously obtained by Gruenberg, Hurley, and Sehgal. 相似文献
996.
John R. Faulkner 《Geometriae Dedicata》1996,60(3):237-275
A new axiomatization involving incidence and remoteness of planes with nondivision coordinate rings is introduced and a coordinatization theorem is obtained. A geometric process of splitting points and lines to obtain another plane with the same coordinates is described. It is also shown that a group of Steinberg type is parametrized by a nonassociative ring. The notion of elementary basis sets for an associative ring is introduced and constructions of projective and affine planes are given. A plane with reflections determining a system of rotations is shown to have commutative, associative coordinates. 相似文献
997.
Ken-Ichi Maruyama 《Topology》2007,46(3):319-341
We study nilpotent subgroups of automorphism groups in the category of groups and the homotopy category of spaces. We establish localization and completion theorems for nilpotent groups of automorphisms of nilpotent groups. We then apply these algebraic theorems to prove analogous results for certain groups of self-homotopy equivalences of spaces. 相似文献
998.
Harm Derksen 《Journal of Pure and Applied Algebra》2007,209(1):91-98
The vanishing ideal I of a subspace arrangement V1∪V2∪?∪Vm⊆V is an intersection I1∩I2∩?∩Im of linear ideals. We give a formula for the Hilbert polynomial of I if the subspaces meet transversally. We also give a formula for the Hilbert series of the product ideal J=I1I2?Im without any assumptions about the subspace arrangement. It turns out that the Hilbert series of J is a combinatorial invariant of the subspace arrangement: it only depends on the intersection lattice and the dimension function. The graded Betti numbers of J are determined by the Hilbert series, so they are combinatorial invariants as well. We will also apply our results to generalized principal component analysis (GPCA), a tool that is useful for computer vision and image processing. 相似文献
999.
Thomas Kailath 《Integral Equations and Operator Theory》1998,30(2):135-139
1000.