共查询到20条相似文献,搜索用时 187 毫秒
1.
Pedro Ricardo López-Bautista Gabriel Daniel Villa-Salvador 《Israel Journal of Mathematics》2000,116(1):345-365
LetL/K be a finite Galoisp-extension of algebraic function fields of one variable over an algebraically closed fieldk of characteristicp, with Galois groupG=Gal(L/K). The space Ώ
L
s
(0) of semisimple holomorphic differentials ofL is thek-vector space of holomorphic differentials which are fixed by the Cartier operator. We obtain the isomorphism classes and
multiplicities of the summands in a Krull-Schmidt decomposition of thek[G]-module Ώ
L
s
(0) into a direct sum of indecomposablek[G]-modules.
Partially supported by CONACyT, project No. 25063-E. 相似文献
2.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2009,7(2):176-185
Let F be a field, A be a vector space over F, and GL(F,A) the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the present article we begin the study of subgroups G of GL(F,A) such that every subspace of A is either nearly G-invariant or almost G-invariant. More precisely, we consider the case when G is a periodic p′-group where p = charF.
相似文献
3.
Let A be a tame concealed or tubular algebra and d the dimension-vector of a periodic module with respect to the action of the Auslander–Reiten translation. We prove that the affine variety mod
A
(d) of all A-modules of dimension-vector d is a normal complete intersection. Moreover, we show that a module M in mod
A
(d) is nonsingular if and only if Ext
A
2(M,M)=0. 相似文献
4.
Let 𝒲 be the Virasoro-like algebra, and d 1, d 2 be the degree derivations of 𝒲. Set ? = W⊕C d 1⊕C d 2. Let F α(V) be the ?-module defined by Larsson's functor applied to a finite dimensional sl 2-module V. In this article, the derivations from ? to ?-modules F α(V) and the first cohomology group H 1(?, F α(V)) are given. 相似文献
5.
Let F be a field and let {d 1,…,dk } be a set of independent indeterminates over F. Let A(d 1,…,dk ) be an n × n matrix each of whose entries is an element of F or a sum of an element of F and one of the indeterminates in {d 1,…,dk }. We assume that no d 1 appears twice in A(d 1,…,dk ). We show that if det A(d 1,…,dk ) = 0 then A(d 1,…,dk ) must contain an r × s submatrix B, with entries in F, so that r + s = n + p and rank B ? p ? 1: for some positive integer p. 相似文献
6.
P. Gabriel L. A. Nazarova A. V. Roiter V. V. Sergeichuk D. Vossieck 《Ukrainian Mathematical Journal》1993,45(3):335-372
Assume thatB is a finite-dimensional algebra over an algebraically closed fieldk, B
d
=Spec k[(B
d
] is the affine algebraic scheme whoseR-points are theB k k[Bd]-module structures onR
d, and Md is a canonical Bk k[Bd]-module supported by k[Bd]d. Further, say that an affine subscheme of Bd isclass true if the functor Fgn X Md k[B] X induces an injection between the sets of isomorphism classes of indecomposable finite-dimensional modules over k[] andB. If Bd contains a class-true plane for somed, then the schemes Be contain class-true subschemes of arbitrary dimensions. Otherwise, each Bd contains a finite number of classtrue puncture straight linesL(d, i) such that for eachn, almost each indecomposableB-module of dimensionn is isomorphic to someF
L(d, i) (X); furthermore,F
L(d, i) (X) is not isomorphic toF
L(l, j) (Y) if(d, i) (l, j) andX 0. The proof uses a reduction to subspace problems, for which an inductive algorithm permits us to prove corresponding statements.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 3, pp. 313–352, March, 1993. 相似文献
7.
LetAbe a path algebra of tame type over a finite field, letMbe an indecomposableA-module, and let (A) be the composition algebra ofA. The main result in this paper is that [M] ∈ (A) if and only ifMis a stone, i.e., Ext1A(M, M) = 0. 相似文献
8.
For a quiver Q, a k-algebra A, and an additive full subcategory 𝒳 of A-mod, the monomorphism category Mon(Q, 𝒳) is introduced. The main result says that if T is an A-module such that there is an exact sequence 0 → T m → … → T 0 → D(A A ) → 0 with each T i ∈ add(T), then Mon(Q, ⊥ T) =⊥(kQ ? k T); and if T is cotilting, then kQ ? k T is a unique cotilting Λ-module, up to multiplicities of indecomposable direct summands, such that Mon(Q, ⊥ T) =⊥(kQ ? k T). As applications, the category of the Gorenstein-projective (kQ ? k A)-modules is characterized as Mon(Q, 𝒢𝒫(A)) if A is Gorenstein; the contravariantly finiteness of Mon(Q, 𝒳) can be described; and a sufficient and necessary condition for Mon(Q, A) being of finite type is given. 相似文献
9.
For flat modules M over a ring A we study the similarities between the three statements,dim k (P) ( k (P)? A M =dfor all prime ideals P of A, the Ap-module M p is free of rank d for all prime ideals P of A, and M is a locally free J4-module of rank d. We have particularly emphasized the case when there is an>l-algebra B, essentially of finite type, and M is a finitely generated B-module. 相似文献
10.
Leonid A. Kurdachenko Alexey V. Sadovnichenko Igor Ya. Subbotin 《Central European Journal of Mathematics》2010,8(2):261-265
Let F be a field, A be a vector space over F, GL(F, A) be the group of all automorphisms of the vector space A. A subspace B of A is called nearly G-invariant, if dim
F
(BFG/B) is finite. A subspace B is called almost G-invariant, if dim
F
(B/Core
G
(B)) is finite. In the current article, we study linear groups G such that every subspace of A is either nearly G-invariant or almost G-invariant in the case when G is a soluble p-group where p = char
F. 相似文献
11.
R.L Vaughn 《Applicable analysis》2013,92(4):337-348
Let L 0(ΩA,P) be the space of equivalent classes of random variables defined on a probability space (Ω,A,P). Let H be the closed subspace of L 0(Ω,A,P) spanned by a sequence of i.i.d. (independent and identically distributed) random variables having the symmetric nondegenerate law F. It is proved that H is linearly homeomorphic to l p for 0<p≤2 if F belongs to the domain of normal attraction of symmetric stable law withexponent p. 相似文献
12.
The p-rank of an algebraic curve X over an algebraically closed field k of characteristic p>0 is the dimension of the vector space H1(Xet,Fp). We study the representations of finite subgroups GAut(X) induced on H1(Xet,Fp)k, and obtain two main results.First, the sum of the nonprojective direct summands of the representation, i.e., its core, is determined explicitly by local data given by the fixed point structure of the group acting on the curve. As a corollary, we derive a congruence formula for the p-rank.Secondly, the multiplicities of the projective direct summands of quotient curves, i.e., their Borne invariants, are calculated in terms of the Borne invariants of the original curve and ramification data. In particular, this is a generalization of both Nakajima's equivariant Deuring–Shafarevich formula and a previous result of Borne in the case of free actions. 相似文献
13.
Eric S. Brussel 《Israel Journal of Mathematics》1996,96(1):141-183
LetF be a discretely Henselian field of rank one, with residue fieldk a number field, and letD/F be anF-division algebra. We conduct an exhaustive study of the decomposability of an arbitraryD. Specifically, we prove the following:D has a semiramified (SR)F-division subalgebra if and only ifD has a totally ramified (TR) subfield. However, there may be TR subfields not contained in any SR subalgebra. IfD has prime-power index, thenD is decomposable if and only ifD properly contains a SR division subalgebra. Equivalently,D has a decomposable Sylow factor if and only if ii(D
⊗n
)≠1/n
i(D) for somen dividing the period ofD, that is, if and only if the index fails to mimic the behavior of the period ofD. There exists indecomposableD with prime-power periodp
2 and indexp
3. Every proper division subalgebra ofD is indecomposable. Conversely, every indecomposableF-division algebra ofp-power index embeds properly in someD ofp-power index if and only ifk does not have a certain strengthened form of class field theory’s Special Case. Semiramified division algebras and division
algebras of odd index always properly embed. Finally, these results apply to an extent overk(t), and we prove that there exist indecomposablek(t)-division algebras of periodp
2 and indexp
3, solving an open problem of Saltman.
Dedicated to the memory of Amitsur
Research supported in part by NSF Grant DMS-9100148. 相似文献
14.
Hans TRIEBEL 《数学学报(英文版)》2008,24(4):539-554
A space Apq^s (R^n) with A : B or A = F and s ∈R, 0 〈 p, q 〈 ∞ either has a trace in Lp(Г), where Г is a compact d-set in R^n with 0 〈 d 〈 n, or D(R^n/Г) is dense in it. Related dichotomy numbers are introduced and calculated. 相似文献
15.
In this paper, we study a tower {A
n
G: n} ≥ 1 of finite-dimensional algebras; here, G represents an arbitrary finite group,d denotes a complex parameter, and the algebraA
n
G(d) has a basis indexed by ‘G-stable equivalence relations’ on a set whereG acts freely and has 2n orbits. We show that the algebraA
n
G(d) is semi-simple for all but a finite set of values ofd, and determine the representation theory (or, equivalently, the decomposition into simple summands) of this algebra in the
‘generic case’. Finally we determine the Bratteli diagram of the tower {A
n
G(d): n} ≥ 1 (in the generic case). 相似文献
16.
Armen Sergeev 《中国科学A辑(英文版)》2009,52(12):2714-2729
We discuss the twistor quantization problem for the classical system (V
d
,A
d
), represented by the phase space V
d
, identified with the Sobolev space H
01/2 (S
1,ℝ
d
) of half-differentiable vector functions on the circle, and the algebra of observables A
d
, identified with the semi-direct product of the Heisenberg algebra of V
d
and the algebra Vect(S
1) of tangent vector fields on the circle. 相似文献
17.
Given a finite family F\mathcal{F} of convex sets in ℝ
d
, we say that F\mathcal{F} has the (p,q)
r
property if for any p convex sets in F\mathcal{F} there are at least r
q-tuples that have nonempty intersection. The piercing number of F\mathcal{F} is the minimum number of points we need to intersect all the sets in F\mathcal{F}. In this paper we will find some bounds for the piercing number of families of convex sets with (p,q)
r
properties. 相似文献
18.
Christophe Breuil 《Israel Journal of Mathematics》2011,182(1):349-382
Let ρ be a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/ℚ
p
) over ̅F
p
. The modulo p Langlands correspondence for GL2(ℚ
p
) defined in [5], as realized in [9], can be reformulated as a quite simple recipee giving back the (φ, Γ)-module of the dual of ρ starting from the “Diamond diagram” associated to ρ. Let F be a finite unramified extension of ℚ
p
and ρ a 2-dimensional continuous semi-simple generic representation of Gal(̅ℚ
p
/F) over ̅F
p
. When one formally extends this recipee to the Diamond diagrams associated to ρ in [6], we show that one essentially finds the (φ, Γ)-module of the tensor induction from F to ℚ
p
of the dual of ρ. 相似文献
19.
Intersection theorems with geometric consequences 总被引:3,自引:0,他引:3
In this paper we prove that ifℱ is a family ofk-subsets of ann-set, μ0, μ1, ..., μs are distinct residues modp (p is a prime) such thatk ≡ μ0 (modp) and forF ≠ F′ ≠ℱ we have |F ∩F′| ≡ μi (modp) for somei, 1 ≦i≦s, then |ℱ|≦(
s
n
).
As a consequence we show that ifR
n
is covered bym sets withm<(1+o(1)) (1.2)
n
then there is one set within which all the distances are realised.
It is left open whether the same conclusion holds for compositep. 相似文献
20.
Let V be an r-dimensional vector space over an infinite field F of prime characteristic p, and let Ln(V) denote the nth homogeneous component of the free Lie algebra on V. We study the structure of Ln(V) as a module for the general linear group GLr(F) when n=pk and k is not divisible by p and where r≥n. Our main result is an explicit 1-1 correspondence, multiplicity-preserving, between the indecomposable direct summands of
Lk(V) and the indecomposable direct summands of Ln(V) which are not isomorphic to direct summands of V⊗n. Our approach uses idempotents of the Solomon descent algebras, and in addition a correspondence theorem for permutation
modules of symmetric groups.
Second author supported by Deutsche Forschungsgemeinschaft (DFG-Scho 799). 相似文献