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1.
A. V. Mikhalev I. N. Balaba S. A. Pikhtilkov 《Journal of Mathematical Sciences》2008,149(2):1146-1156
In this paper, we introduce the class of graded Ω-groups, which includes: groups; associative, conformal and vertex algebras;
Lie algebras and graded algebras. The graded prime radical of a graded Ω-group is defined, and its elementwise characterization
is given. It is shown that the graded prime radical of a graded Ω-groups with a finiteness condition coincides with the lower
weakly solvable (in the Parfyonov sense) radical.
__________
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 159–174, 2006. 相似文献
2.
Homogeneous graded metrics over split ℤ2-graded manifolds whose Levi-Civita connection is adapted to a given splitting, in the sense recently introduced by Koszul,
are completely described. A subclass of such is singled out by the vanishing of certain components of the graded curvature
tensor, a condition that plays a role similar to the closedness of a graded symplectic form in graded symplectic geometry:
It amounts to determining a graded metric by the data {g, ω, Δ′}, whereg is a metric tensor onM, ω 0 is a fibered nondegenerate skewsymmetric bilinear form on the
Batchelor bundleE → M, and Δ′ is a connection onE satisfying Δ′ω = 0. Odd metrics are also studied under the same criterion and they are specified by the data {κ, Δ′}, with
κ ∈ Hom (TM, E) invertible, and Δ′κ = 0. It is shown in general that even graded metrics of constant graded curvature can be supported only
over a Riemannian manifold of constant curvature, and the curvature of Δ′ onE satisfiesR
Δ′ (X,Y)2 = 0. It is shown that graded Ricci flat even metrics are supported over Ricci flat manifolds and the curvature of the connection
Δ′ satisfies a specific set of equations. 0 Finally,
graded Einstein even metrics can be supported only over Ricci flat Riemannian manifolds. Related results for graded metrics
on Ω(M) are also discussed.
Partially supported by DGICYT grants #PB94-0972, and SAB94-0311; IVEI grant 95-031; CONACyT grant #3189-E9307. 相似文献
3.
The Maximal Graded Left Quotient Algebra of a Graded Algebra1) 总被引:1,自引:0,他引:1
Gonzalo ARANDA PINO Mercedes SILES MOLINA 《数学学报(英文版)》2006,22(1):261-270
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra. 相似文献
4.
We study the graded Poisson structures defined on Ω(M), the graded algebra of differential forms on a smooth manifoldM, such that the exterior derivative is a Poisson derivation. We show that they are the odd Poisson structures previously studied
by Koszul, that arise from Poisson structures onM. Analogously, we characterize all the graded symplectic forms on ΩM) for which the exterior derivative is a Hamiltomian graded vector field. Finally, we determine the topological obstructions
to the possibility of obtaining all odd symplectic forms with this property as the image by the pullback of an automorphism
of Ω(M) of a graded symplectic form of degree 1 with respect to which the exterior derivative is a Hamiltonian graded vector field. 相似文献
5.
We use the correspondence between hypergraphs and their associated edge ideals to study the minimal graded free resolution
of squarefree monomial ideals. The theme of this paper is to understand how the combinatorial structure of a hypergraph ℋ
appears within the resolution of its edge ideal ℐ(ℋ). We discuss when recursive formulas to compute the graded Betti numbers
of ℐ(ℋ) in terms of its sub-hypergraphs can be obtained; these results generalize our previous work (Hà, H.T., Van Tuyl, A.
in J. Algebra 309:405–425, 2007) on the edge ideals of simple graphs. We introduce a class of hypergraphs, which we call properly-connected, that naturally
generalizes simple graphs from the point of view that distances between intersecting edges are “well behaved.” For such a
hypergraph ℋ (and thus, for any simple graph), we give a lower bound for the regularity of ℐ(ℋ) via combinatorial information
describing ℋ and an upper bound for the regularity when ℋ=G is a simple graph. We also introduce triangulated hypergraphs that are properly-connected hypergraphs generalizing chordal
graphs. When ℋ is a triangulated hypergraph, we explicitly compute the regularity of ℐ(ℋ) and show that the graded Betti numbers
of ℐ(ℋ) are independent of the ground field. As a consequence, many known results about the graded Betti numbers of forests
can now be extended to chordal graphs.
Dedicated to Anthony V. Geramita on the occasion of his 65th birthday. 相似文献
6.
In the case of finite groups, a separating algebra is a subalgebra of the ring of invariants which separates the orbits. Although
separating algebras are often better behaved than the ring of invariants, we show that many of the criteria which imply the
ring of invariants is non-Cohen–Macaulay actually imply that no graded separating algebra is Cohen–Macaulay. For example,
we show that, over a field of positive characteristic p, given sufficiently many copies of a faithful modular representation,
no graded separating algebra is Cohen–Macaulay. Furthermore, we show that, for a p-group, the existence of a Cohen–Macaulay graded separating algebra implies the group is generated by bireections. Additionally,
we give an example which shows that Cohen–Macaulay separating algebras can occur when the ring of invariants is not Cohen–Macaulay. 相似文献
7.
Luchezar L. Avramov Ragnar-Olaf Buchweitz Srikanth Iyengar 《Inventiones Mathematicae》2007,169(1):1-35
A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules
over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class – a substitute
for the length of a free complex – and on the rank of a differential module in terms of invariants of its homology. These
results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization
of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes
over commutative noetherian rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings. 相似文献
8.
In this paper, we describe ∈-derivations in certain graded algebras by their actions on elements satisfying some special conditions. One of the main results is applied to local ∈-derivations on some certain graded algebras. 相似文献
9.
TheRelativePropertiesofGradedRingRand SmashProductR#GWeiJunchao(魏俊潮);LiLibin(李立斌)(YangzhouInstituteofTechnology,Yangzhou,2250... 相似文献
10.
H. Gopalakrishnan 《Semigroup Forum》2001,62(1):146-158
\noindent We find the index of nilpotency of a strong supplementary semilattice sum of rings, R=\tdsp\sum
α∈ Y
R
α
, where Y is a semilattice, when each R
α
has index of nilpotency≤ k . Then we find the index of nilpotency of R when it is graded over a rectangular band Y and each R
α
has index of nilpotency≤ k . These results are generalized to normal band graded rings. Further, we find sufficient conditions for a ring graded by
a semilattice of nilpotent semigroups to have bounded index of nilpotency. We also show by examples that these conditions
are necessary in some cases. 相似文献
11.
We determine the maximal graded subalgebras of affine Kac-Moody algebras. We also show that the maximal graded subalgebras
of loop algebras are essentially loop algebras.
Supported by the Binational Science Foundation United States — Israel, Grant No. 92-00034. 相似文献
12.
Modules of harmonic cochains on the Bruhat-Tits building of the projective general linear group over ap-adic field were defined by one of the authors, and were shown to represent the cohomology of Drinfel’d’sp-adic symmetric domain. Here we define certain non-trivial natural extensions of these modules and study their properties.
In particular, for a quotient of Drinfel’d’s space by a discrete cocompact group, we are able to define maps between consecutive
graded pieces of its de Rham cohomology, which we show to be (essentially) isomorphisms. We believe that these maps are graded
versions of the Hyodo-Kato monodromy operatorN. 相似文献
13.
Given an affine domain of GelfandKirillov dimension 2over an algebraically closed field, it is shown that the centralizerof any non-scalar element of this domain is a commutative domainof GelfandKirillov dimension 1 whenever the domain isnot polynomial identity. It is shown that the maximal subfieldsof the quotient division ring of a finitely graded Goldie algebraof GelfandKirillov dimension 2 over a field F all havetranscendence degree 1 over F. Finally, centralizers of elementsin a finitely graded Goldie domain of GelfandKirillovdimension 2 over an algebraically closed field are considered.In this case, it is shown that the centralizer of a non-scalarelement is an affine commutative domain of GelfandKirillovdimension 1. 2000 Mathematics Subject Classification 16P90. 相似文献
14.
We obtain criteria that answer the question of when an isomorphism of graded endomorphism rings of strong gr-generators is
induced by a gr-generator, graded Morita equivalence, or semi-linear isomorphism.
Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 5, pp. 3–18, 2007. 相似文献
15.
We introduce group corings, and study functors between categories of comodules over group corings, and the relationship to
graded modules over graded rings. Galois group corings are defined, and a Structure Theorem for the G-comodules over a Galois group coring is given. We study (graded) Morita contexts associated to a group coring. Our theory
is applied to group corings associated to a comodule algebra over a Hopf group coalgebra.
This research was supported by the research project G.0622.06 “Deformation quantization methods for algebras and categories
with applications to quantum mechanics” from Fonds Wetenschappelijk Onderzoek-Vlaanderen. The third author was partially supported
by the SRF (20060286006) and the FNS (10571026). 相似文献
16.
We describe primary graded groups (in particular, locally graded, RN-groups) with complementable non-Frattini subgroups.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 10, pp. 1324–1333, October, 1999. 相似文献
17.
Graded rings and essential ideals 总被引:1,自引:0,他引:1
LetG be a group andA aG-graded ring. A (graded) idealI ofA is (graded) essential ifI⊃J≠0 wheneverJ is a nonzero (graded) ideal ofA. In this paper we study the relationship between graded essential ideals ofA, essential ideals of the identity componentA
e
and essential ideals of the smash productA#G
*. We apply our results to prime essential rings, irredundant subdirect sums and essentially nilpotent rings. 相似文献
18.
19.
Among all the homogeneous Riemannian graded metrics on the algebra of differential forms, those for which the exterior derivative
is a Killing graded vector field are characterized. It is shown that all of them are odd, and are naturally associated to
an underlying smooth Riemannian metric. It is also shown that all of them are Ricci-flat in the graded sense, and have a graded
Laplacian operator that annihilates the whole algebra of differential forms.
Partially supported by DGICYT grants #PB91-0324, and SAB94-0311; CONACyT grant #3189-E9307. 相似文献
20.
We say that an algebra R, graded by a group, is graded reversible if ab=0 implies ba=0 where a,b are homogeneous elements of R. In this note, we study graded reversibility when R=ℤG (viewed as a ℤ-algebra) and the grading group is cyclic of order two. A complete characterization of when this occurs is
obtained for some classes of groups (including dihedral groups) assuming a positive answer to an open question concerning
group gradings. 相似文献