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1.
Kamran Divaani-Aazar 《Proceedings Mathematical Sciences》2009,119(1):23-35
Let R be a (not necessarily local) Noetherian ring and M a finitely generated R-module of finite dimension d. Let be an ideal of R and denote the intersection of all prime ideals . It is shown that
where for an Artinian R-module A we put
A. As a consequence, it is proved that for all ideals of R, there are only finitely many non-isomorphic top local cohomology modules having the same support. In addition, we establish an analogue of the Lichtenbaum-Hartshorne vanishing theorem over rings
that need not be local. 相似文献
2.
Niels Grønbæk 《Proceedings Mathematical Sciences》2008,118(2):235-243
Let be a Banach algebra and let X be a Banach -bimodule. In studying (,X) it is often useful to extend a given derivation D: → X to a Banach algebra containing as an ideal, thereby exploiting (or establishing) hereditary properties. This is usually done using (bounded/unbounded) approximate
identities to obtain the extension as a limit of operators b ↦ D(ba) − b.D(a), a ε in an appropriate operator topology, the main point in the proof being to show that the limit map is in fact a derivation.
In this paper we make clear which part of this approach is analytic and which algebraic by presenting an algebraic scheme
that gives derivations in all situations at the cost of enlarging the module. We use our construction to give improvements
and shorter proofs of some results from the literature and to give a necessary and sufficient condition that biprojectivity
and biflatness is inherited to ideals. 相似文献
3.
Debashish Goswami 《Proceedings Mathematical Sciences》2009,119(1):63-70
We prove that an arbitrary (not necessarily countably generated) Hilbert G - module on a G - C
* algebra admits an equivariant embedding into a trivial G - module, provided G is a compact Lie group and its action on is ergodic. 相似文献
4.
Changguo Wei 《Proceedings Mathematical Sciences》2008,118(4):517-524
Some results on A
-algebras are given. We study the problem when ideals, quotients and hereditary subalgebras of A
-algebras are A
-algebras or A
-algebras, and give a necessary and sufficient condition of a hereditary subalgebra of an A
-algebra being an A
-algebra. 相似文献
5.
Given two vectors x, y in a Hilbert space and a weakly closed -module , we provide a necessary and sufficient condition for the existence of a compact operator T in satisfying Tx = y. 相似文献
6.
In this paper we mainly study the derivations for even part of the finite-dimensional odd Hamiltonian superalgebra HO over a field of prime characteristic. We first give the generating set of the even part g of HO. Then we compute the derivations from g into the even part m of the generalized Witt superalgebra. Finally, we determine the derivation algebra and outer derivation algebra of and the dimension formulas. In particular, the first cohomology groups H^1(g;m) and H^1(g;g) are determined. 相似文献
7.
Let G be the complex general linear group and its Lie algebra equipped with a factorizable Lie bialgebra structure; let Uħ() be the corresponding quantum group. We construct explicit Uħ()-equivariant quantization of Poisson orbit bundles O
λ → O
μ in *. 相似文献
8.
Concettina Galati 《Rendiconti del Circolo Matematico di Palermo》2009,58(2):211-243
Let be a smooth family of surfaces whose general fibre is a smooth surface of ℙ3 and whose special fibre has two smooth components, intersecting transversally along a smooth curve R. We consider the Universal Severi-Enriques variety on . The general fibre of is the variety of curves on in the linear system with k cusps and δ nodes as singularities. Our problem is to find all irreducible components of the special fibre of . In this paper, we consider only the cases (k, δ) = (0, 1) and (k, δ) = (1, 0). In particular, we determine all singular curves on the special fibre of which, counted with the right multiplicity, are a limit of 1-cuspidal curves on the general fibre of .
相似文献
9.
A Fitting class $ \mathfrak{F} A Fitting class is said to be π-maximal if is an inclusion maximal subclass of the Fitting class of all finite soluble π-groups. We prove that is a π-maximal Fitting class exactly when there is a prime p ∊ π such that the index of the -radical in G is equal to 1 or p for every π-subgroup of G. Hence, there exist maximal subclasses in a local Fitting class. This gives a negative answer to Skiba’s conjecture that
there are no maximal Fitting subclasses in a local Fitting class (see [1, Question 13.50]).
Original Russian Text Copyright ? 2008 Savelyeva N. V. and Vorob’ev N. T.
__________
Vitebsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 6, pp. 1411–1419, November–December, 2008. 相似文献
10.
V. L. Popov 《Proceedings of the Steklov Institute of Mathematics》2009,264(1):146-158
Let G be a connected linear algebraic group, let V be a finite dimensional algebraic G-module, and let and be two G-orbits in V. We describe a constructive way to find out whether or not lies in the closure of .
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2009, Vol. 264, pp. 152–164.
In memory of V.A. Iskovskikh 相似文献
11.
E. Ekici 《Acta Mathematica Hungarica》2007,117(4):325-333
The main purpose of this paper is to introduce the concepts of *-sets, *-continuous functions and to obtain new decompositions of continuous and ηζ-continuous functions. Moreover, properties of *-sets and some properties of -sets are discussed.
相似文献
12.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献
13.
Let be a finite field with q elements, where q is a prime power. Let G be a subgroup of the general linear group over and be the rational function field over . We seek to understand the structure of the rational invariant subfield . In this paper, we prove that is rational (or, purely transcendental) by giving an explicit set of generators when G is the symplectic group. In particular, the set of generators we gave satisfies the Dickson property.
相似文献
14.
We classify the maximal irreducible periodic subgroups of PGL(q,
), where
is a field of positive characteristic p transcendental over its prime subfield, q = p is prime, and
× has an element of order q. That is, we construct a list of irreducible subgroups G of GL(q,
) containing the centre
×1
q
of GL(q,
), such that G/
×1
q
is a maximal periodic subgroup of PGL(q,
), and if H is another group of this kind then H is GL(q,
)-conjugate to a group in the list. We give criteria for determining when two listed groups are conjugate, and show that a
maximal irreducible periodic subgroup of PGL(q,
) is self-normalising.
相似文献
15.
Ján Jakubík 《Czechoslovak Mathematical Journal》2008,58(3):833-848
Let be an infinite cardinal. We denote by the collection of all -representable Boolean algebras. Further, let be the collection of all generalized Boolean algebras B such that for each b ∈ B, the interval [0, b] of B belongs to . In this paper we prove that is a radical class of generalized Boolean algebras. Further, we investigate some related questions concerning lattice ordered
groups and generalized MV-algebras.
This work was supported by Science and Technology Assistance Agency under the contract No. APVT-51-032002.
This work has been partially supported by the Slovak Academy of Sciences via the project Center of Excellence-Physics of Information. 相似文献
16.
Let H olenote a complex separable Hilbert space and L(H) denote the collection of bounded linear operators on H. An operator T ∈ L(H) is said to be strongly irreducible if T does not commute with any nontrivial idempotent. Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum. This result can be considered as an approximate inverse of the Riesz decomposition theorem. In the paper, we give a more precise charact... 相似文献
17.
A set of positive integers is a perfect difference set if every nonzero integer has a unique representation as the difference of two elements of . We construct dense perfect difference sets from dense Sidon sets. As a consequence of this new approach we prove that there exists a perfect difference set such that
.
Also we prove that there exists a perfect difference set
such that
A(x)/≥ 1/.
The work of J. C. was supported by Grant MTM 2005-04730 of MYCIT (Spain).
The work of M. B. N. was supported in part by grants from the NSA Mathematical Sciences Program and the PSC-CUNY Research
Award Program. 相似文献
18.
Binyong Sun 《Israel Journal of Mathematics》2009,170(1):395-410
Let G be a semisimple Lie group with a Cartan decomposition G = K exp(). For every finite-dimensional representation of G, there is an inner product on the representation space such that with respect to it, K acts as unitary operators, and exp() acts as positive definite Hermitian operators. In this paper, we observe that similar phenomena appear for infinite-dimensional
representations with real infinitesimal characters.
Supported by Tianyuan Mathematics Foundation of NSFC (Grant No. 10626050). 相似文献
19.
WenMing Wu 《中国科学A辑(英文版)》2008,51(11):2081-2088
Given the hyperbolic measure dxdy/y
2 on the upper half plane ℍ, the rational actions of PSL2(ℝ) on ℍ induces a continuous unitary representation α of this group on the Hilbert space L
2(ℍ, dxdy/y
2). Supposing that = {M
f
: f ∈ L
∞ (ℍ, dxdy/y
2)}, we show that the crossed product is of type I. In fact, the crossed product is *-isomorphic to the von Neumann algebra , where is the abelian group von Neumann algebra generated by the left regular representation of K.
This work was supported by the Youth Foundation of Sichuan Education Department of China (Grant No. 2003B017) 相似文献
20.
Nuria Corral 《Bulletin of the Brazilian Mathematical Society》2009,40(2):181-224
The polar curves of foliations having a curve C of separatrices generalize the classical polar curves associated to hamiltonian foliations of C. As in the classical theory, the equisingularity type ℘() of a generic polar curve depends on the analytical type of , and hence of C. In this paper we find the equisingularity types ε(C) of C, that we call kind singularities, such that ℘() is completely determined by ε(C) for Zariski-general foliations . Our proofs are mainly based on the adjunction properties of the polar curves. The foliation-like framework is necessary,
otherwise we do not get the right concept of general foliation in Zariski sense and, as we show by examples, the hamiltonian
case can be out of the set of general foliations.
The author was partially supported by the research projects MTM2007-66262 (Ministerio de Educación y Ciencia), MTM2006-15338-C02-02
(Ministerio de Educación y Ciencia),VA059A07 (Junta de Castilla y León) and PGIDITI06PXIB377128PR (Xunta de Galicia). 相似文献