共查询到20条相似文献,搜索用时 15 毫秒
1.
Ehud Meir 《Algebras and Representation Theory》2012,15(2):391-405
We define a notion of complexity for modules over group rings of infinite groups. This generalizes the notion of complexity
for modules over group algebras of finite groups. We show that if M is a module over the group ring kG, where k is any ring and G is any group, and M has f-complexity (where f is some complexity function) over some set of finite index subgroups of G, then M has f-complexity over G (up to a direct summand). This generalizes the Alperin-Evens Theorem, which states that if the group G is finite then the complexity of M over G is the maximal complexity of M over an elementary abelian subgroup of G. We also show how we can use this generalization in order to construct projective resolutions for the integral special linear
groups, SL(n, ℤ), where n ≥ 2. 相似文献
2.
Let X be a compact connected Kähler manifold such that the holomorphic tangent bundle TX is numerically effective. A theorem of Demailly et al. (1994) [11] says that there is a finite unramified Galois covering M→X, a complex torus T, and a holomorphic surjective submersion f:M→T, such that the fibers of f are Fano manifolds with numerically effective tangent bundle. A conjecture of Campana and Peternell says that the fibers of f are rational and homogeneous. Assume that X admits a holomorphic Cartan geometry. We prove that the fibers of f are rational homogeneous varieties. We also prove that the holomorphic principal G-bundle over T given by f, where G is the group of all holomorphic automorphisms of a fiber, admits a flat holomorphic connection. 相似文献
3.
Christian Neumaier 《Archiv der Mathematik》2005,85(6):497-507
Let 〈G, +〉 be a finite (not necessarily abelian) group. Then M0(G) := {f : G → G| f (0) = 0} is a near-ring, i.e., a group which is also closed under composition of functions. In Theorem 4.1 we give lower
and upper bounds for the fraction of the bijections which generate the near-ring M0(G). From these bounds we conclude the following: If G has few involutions and the order of G is large, then a high fraction of the bijections generate the near-ring M0(G). Also the converse holds: If a high fraction of the bijections generate M0(G), then G has few involutions (compared to the order of G).
Received: 10 January 2005 相似文献
4.
Timothy J. Ford 《代数通讯》2013,41(9):3277-3298
We study algebra classes and divisor classes on a normal affine surface of the form z 2 = f(x, y). The affine coordinate ring is T = k[x, y, z]/(z 2 ? f), and if R = k[x, y][f ?1] and S = R[z]/(z 2 ? f), then S is a quadratic Galois extension of R. If the Galois group is G, we show that the natural map H1(G, Cl(T)) → H1(G, Pic(S)) factors through the relative Brauer group B(S/R) and that all of the maps are onto. Sufficient conditions are given for H1(G, Cl(T)) to be isomorphic to B(S/R). The groups and maps are computed for several examples. 相似文献
5.
Jan Jaworowski 《Journal of Fixed Point Theory and Applications》2007,1(1):111-121
Suppose that G is a compact Lie group, M and N are orientable, free G-manifolds and f : M → N is an equivariant map. We show that the degree of f satisfies a formula involving data given by the classifying maps of the orbit spaces M/G and N/G. In particular, if the generator of the top dimensional cohomology of M/G with integer coefficients is in the image of the cohomology map induced by the classifying map for M, then the degree is one.
The condition that the map be equivariant can be relaxed: it is enough to require that it be “nearly equivariant”, up to a
positive constant. We will also discuss the G-average construction and show that the requirement that the map be equivariant can be replaced by a somewhat weaker condition
involving the average of the map.
These results are applied to maps into real, complex and quaternionic Stiefel manifolds. In particular, we show that a nearly
equivariant map of a complex or quaternionic Stiefel manifold into itself has degree one.
Dedicated to the memory of Jean Leray 相似文献
6.
Antoinette Jourdain 《Annals of Global Analysis and Geometry》2001,19(1):11-34
Given (M, g
0) a three-dimensional compact Riemannian manifold, assumed not to be conformally diffeomorphic to the standard unit 3-sphere, and G a compactsubgroup of the conformal group of (M, g
0), we first study conditions for a smooth G-invariant function f to be the scalar curvature of a G-invariant conformalmetric to g
0. Then, extending previous results of Hebeyand Vaugon, we study conditions for f to be the scalarcurvature of at least two conformal metrics to g
0. 相似文献
7.
Andrés Pedroza 《Differential Geometry and its Applications》2008,26(5):503-507
Let (M,ω) be a symplectic manifold and G a compact Lie group that acts on M. Assume that the action of G on M is Hamiltonian. Then a G-equivariant Hamiltonian map on M induces a map on the symplectic quotient of M by G. Consider an autonomous Hamiltonian H with compact support on M, with no non-constant closed trajectory in time less than 1 and time-1 map fH. If the map fH descends to the symplectic quotient to a map Φ(fH) and the symplectic manifold M is exact and Ham(M,ω) has no short loops, we prove that the Hofer norm of the induced map Φ(fH) is bounded above by the Hofer norm of fH. 相似文献
8.
Peter Wong 《manuscripta mathematica》1999,98(2):243-254
Let f,g:X→M be maps between two closed connected orientable n-manifolds where M=G/K is the homogeneous space of left cosets of a compact connected Lie group G by a finite subgroup K. In this note, we obtain a simple formula for the Lefschetz coincidence number L(f,g) in terms of topological degree, generalizing some previously known formulas for fixed points. Our approach, by means of
Nielsen root theory, also allows us to give a simpler and more geometric proof of the fact that all coincidence classes of
f and g have coincidence index of the same sign.
Received: 3 March 1998 / Revised version: 29 June 1998 相似文献
9.
For any group G such that G is a right R-module for some ring R, the elements of R act on G as endomorphisms and we obtain the near-ring of R-homogeneous maps on G: MR(G) = {f: G → G|f(ga) = f(g)a for all a ∈ R, g ∈ G}. In the special case that R is a topological ring and G is a topological R-module, we study NR(G): = {f ∈ MR(G)|f is continuous}. In particular, we investigate primeness of the near-ring NR(G) of continuous homogeneous maps on G. 相似文献
10.
David S. Herscovici 《Journal of Graph Theory》2003,42(2):141-154
Chung defined a pebbling move on a graph G to be the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. The pebbling number of a connected graph is the smallest number f(G) such that any distribution of f(G) pebbles on G allows one pebble to be moved to any specified, but arbitrary vertex by a sequence of pebbling moves. Graham conjectured that for any connected graphs G and H, f(G×H)≤ f(G)f(H). We prove Graham's conjecture when G is a cycle for a variety of graphs H, including all cycles. © 2002 Wiley Periodicals, Inc. J Graph Theory 42: 141–154, 2003 相似文献
11.
José A. de la Peña 《Linear and Multilinear Algebra》2013,61(7):641-649
A cleavage of a finite graph G is a morphism f : H → G of graphs such that if P is the m × n characteristic matrix defined as P ik = 1 if i ∈ f ?1(k), otherwise = 0, then A(H)P ≤ PA(G), where A(G) and A(H) are the adjacency matrices of G and H, respectively. This concept generalizes induced subgraphs, quotients of graphs, Galois covers, path-tree graphs and others. We show that for spectral radii we have the inequality ρ(H) ≤ ρ(G). Equality holds only in case f : H → G is an equivariant quotient and H has isoperimetric constant i(H) = 0. 相似文献
12.
We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G 0 = G 1 · ··· · G r , where each G i is a simple group of type A?, C?, D?, E6, or E7, we construct a differential equation over C(x) having Galois group G. 相似文献
13.
Consider a Riemannian manifold M which is a Galois covering of a compact manifold, with nilpotent deck transformation group G. For the Laplace operator on M, we prove a precise estimate for the gradient of the heat kernel, and show that the Riesz transforms are bounded in Lp(M), 1 < p < . We also obtain estimates for discrete oscillations of the heat kernel, and boundedness of discrete Riesz transform operators, which are defined using the action of G on M.Mathematics Subject Classification (2000): 58J35, 35B65, 42B20in final form: 8 August 2003 相似文献
14.
《代数通讯》2013,41(9):4079-4094
Let AMB be a QF-bimodule, A a left Artinian ring, B a right Artinian ring, G a semigroup with a unit element (a monoid). Let MG be the set of all functions on G with values in M. Consider MG as an (AG, BG)-bimodule over the semigroup rings AG and BG. It is proved that the annihilator maps I → rMG (I) and R → lAG (R) are mutually inverse bijective Galois correspondences between the set of finitely cogenerated left ideals I ? AG and the set of right BG-submodules R ? MG finitely generated over B. The maps J → lMG (J) and L → rAG (L) are mutually inverse bijective Galois correspondences between the set of finitely cogenerated right ideals J ? AG and the set of left AG-submodules L ? MG finitely generated over A. This result also makes it possible, starting from a given QF-bimodule A MB , to construct new QF-bimodules AG/ISBG/J as bimodules of functions on a semigroup with values in M. 相似文献
15.
Let M be a map on a surface F
2. A geometric realization of M is an embedding of F
2 into a Euclidian 3-space ℝ3 with no self-intersection such that each face of M is a flat polygon. In Bonnington and Nakamoto (Discrete Comput. Geom. 40:141–157, 2008), it has been proved that every triangulation G on the projective plane has a face f such that the triangulation G−f on the M?bius band obtained from G by removing the interior of f has a geometric realization. In this paper, we shall characterize such a face f of G. 相似文献
16.
For simple graphs G and H, let f(G,H) denote the least integer N such that every coloring of the edges of KN contains either a monochromatic copy of G or a rainbow copy of H. Here we investigate f(G,H) when H = Pk. We show that even if the number of colors is unrestricted when defining f(G,H), the function f(G,Pk), for k = 4 and 5, equals the (k ? 2)‐ coloring diagonal Ramsey number of G. © 2006 Wiley Periodicals, Inc. J Graph Theory 相似文献
17.
Sanming Zhou 《Czechoslovak Mathematical Journal》2000,50(2):321-330
Let f be an integer-valued function defined on the vertex set V(G) of a graph G. A subset D of V(G) is an f-dominating set if each vertex x outside D is adjacent to at least f(x) vertices in D. The minimum number of vertices in an f-dominating set is defined to be the f-domination number, denoted by
f
(G). In a similar way one can define the connected and total f-domination numbers
c,f
(G) and
t,f
(G). If f(x) = 1 for all vertices x, then these are the ordinary domination number, connected domination number and total domination number of G, respectively. In this paper we prove some inequalities involving
f
(G),
c,f
(G),
t,f
(G) and the independence domination number i(G). In particular, several known results are generalized. 相似文献
18.
We say that a square matrix M is a degree matrix of a given graph G if there is a so called equitable partition of its vertices into r blocks such that whenever two vertices belong to the same block, they have the same number of neighbors inside any block.We ask now whether for a given degree matrix M, there exists a graph G such that M is a degree matrix of G, and in addition, for any two edges e, f spanning between the same pair of blocks there exists an automorphism of G that sends e to f. In this work, we fully characterize the matrices for which such a graph exists and show a way to construct one. 相似文献
19.
LetG be ap-vertex planar graph having a representation in the plane with nontriangular facesF
1,F
2, …,F
r. Letf
1,f
2, …,f
r denote the lengths of the cycles bounding the facesF
1,F
2, …,F
r respectively. LetC
3(G) be the number of cycles of length three inG. We give bounds onC
3(G) in terms ofp,f
1,f
2, …,f
r. WhenG is 3-connected these bounds are bounds for the number of triangles in a polyhedron. We also show that all possible values
ofC
3(G) between the maximum and minimum value are actually achieved.
This research was supported in part by the U.S.A.F. Office of Scientific Research, Systems Command, under Grant AFOSR-76-3017
and the National Science Foundation under Grant ENG79-09724. 相似文献
20.
Let k be a positive integer. A Roman k-dominating function on a graph G is a labeling f: V (G) → {0, 1, 2} such that every vertex with label 0 has at least k neighbors with label 2. A set {f
1, f
2, …, f
d
} of distinct Roman k-dominating functions on G with the property that Σ
i=1
d
f
i
(v) ≤ 2 for each v ∈ V (G), is called a Roman k-dominating family (of functions) on G. The maximum number of functions in a Roman k-dominating family on G is the Roman k-domatic number of G, denoted by d
kR
(G). Note that the Roman 1-domatic number d
1R
(G) is the usual Roman domatic number d
R
(G). In this paper we initiate the study of the Roman k-domatic number in graphs and we present sharp bounds for d
kR
(G). In addition, we determine the Roman k-domatic number of some graphs. Some of our results extend those given by Sheikholeslami and Volkmann in 2010 for the Roman
domatic number. 相似文献