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1.
Lea Terracini 《Compositio Mathematica》2003,137(1):23-47
Let &ell >3 be a prime. Fix a regular character of F&2
× of order &–1, and an integer M prime to &. Let fS
2(0(M&2)) be a newform which is supercuspidal of type at &. For an indefinite quaternion algebra over Q of discriminant dividing the level of f, there is a local quaternionic Hecke algebra T of type associated to f. The algebra T acts on a quaternionic cohomological module M. We construct a Taylor–Wiles system for M, and prove that T is the universal object for a deformation problem (of type at & and semi-stable outside) of the Galois representation ¯
f
over F¯& associated to f; that T is complete intersection and that the module M is free of rank 2 over T. We deduce a relation between the quaternionic congruence ideal of type for f and the classical one. 相似文献
2.
Following our approach to metric Lie algebras developed in a previous paper we propose a way of understanding pseudo-Riemannian
symmetric spaces which are not semisimple. We introduce cohomology sets (called quadratic cohomology) associated with orthogonal
modules of Lie algebras with involution. Then we construct a functorial assignment which sends a pseudo-Riemannian symmetric
space M to a triple consisting of:
That leads to a classification scheme of indecomposable nonsimple pseudo-Riemannian symmetric spaces. In addition, we obtain
a full classification of symmetric spaces of index 2 (thereby completing and correcting in part earlier classification results
due to Cahen and Parker and to Neukirchner). 相似文献
(i) a Lie algebra with involution (of dimension much smaller than the dimension of the transvection group of M); | |
(ii) a semisimple orthogonal module of the Lie algebra with involution; and | |
(iii) a quadratic cohomology class of this module. |
3.
Let A be an absolute valued algebra containing a nonzero central element a. We prove that A is finite dimensional in the two following cases :
1. |
A satisfies the identity (x2, x, x) = 0, 相似文献
4.
T. E. Armstrong 《International Journal of Game Theory》1991,20(1):65-90
We consider games in coalition function form on a, generally infinite, algebra of coalitions. For finite algebras the additive part mappingv E(v ¦) is the usual. The concern here is the analogue for infinite algebras. The useful construction is the finitely additive stochastic process of additive parts of the game on the filtration
f
of finite subalgebras of.It is shown that
is an isomorphism between:
5.
A. S. Sivatski 《Journal of Mathematical Sciences》2007,145(1):4823-4830
The main purpose of the paper is to strengthen previous author’s results. Let k be a field of characteristic ≠ 2, n ≥ 2. Suppose
that elements
are linearly independent over ℤ/2ℤ. We construct a field extension K/k and a quaternion algebra D = (u, v) over K such that
6.
It is proved that any cluster-tilted algebra defined in the cluster category 𝒞(H) has the same representation type as the initial hereditary algebra H. For any valued quiver (Γ, Ω), an injection from the subset 𝒫?(Ω) of the cluster category 𝒞(Ω) consisting of indecomposable preprojective objects, preinjective objects, and the first shifts of indecomposable projective modules to the set of cluster variables of the corresponding cluster algebra 𝒜Ω is given. The images are called “preprojective cluster variables”. It is proved that all preprojective cluster variables other than ui have denominators u dim M in their irreducible fractions of integral polynomials, where M is the corresponding preprojective module or preinjective module. In case the valued quiver (Γ, Ω) is of finite type, the denominator theorem holds with respect to any cluster. Namely, let x = (x1,…, xn) be a cluster of the cluster algebra 𝒜Ω, and V the cluster tilting object in 𝒞(Ω) corresponding to x, whose endomorphism algebra is denoted by Λ. Then the denominator of any cluster variable y other than xi is x dim M, where M is the indecomposable Λ-module corresponding to y. This result is a generalization of the corresponding result of Caldero–Chapoton–Schiffler to the non-simply-laced case. 相似文献
7.
M. J. Pelling 《Aequationes Mathematicae》1989,37(1):15-37
Thepositive half A
+ of an ordered abelian groupA is the set {x Ax 0} andM
A
+ is amodule if for allx, y M alsox + y, |x – y| M. If A
+
\M thenM() is the module generated byM and. S
M isunbounded inM if(x M)(y S)(x y) and isdense inM if (x1, x2 M)(y S) (x1 <>2 x1 y x2). IfM is a module, or a subgroup of any abelian group, a real-valuedg: M R issubadditive ifg(x + y) g(x) + g(y) for allx, y M. The following hold:
8.
Shigeru Haruki 《Aequationes Mathematicae》1988,36(1):20-31
We give the general solution of the nonsymmetric partial difference functional equationf(x + t,y) + f(x – t,y) – 2f(x,y)/t
2 =f(x,y + s) + f(x,y – s) – 2f(x,y)/s
2 (N) analogous to the well-known wave equation (
2/x
2
–
2/y
2)f(x,y) = 0 with the aid of generalized polynomials when no regularity assumptions are imposed onf. The result is as follows.
Theorem.Let R be the set of all real numbers. A function f: R × R R satisfies the functional equation (N)for all x, y R, s, t R\{0}, and s t if and only if there exist
9.
K. Petras 《Acta Mathematica Hungarica》1999,83(3):241-250
Denote by R
n
G
the remainder functional of the Gaussian quadrature formula involving n nodes. Using an elementary method, we derive the asymptotically best possible inequalities
10.
It is shown that the algebra of the multipliers of the space p (1<<) contains the closed subalgebra Cp+H
p
, which coincides with the Douglas algebra C + H for =2. It is proved that a Toeplitz operator with symbol from Cp+H
p
is Fredholm on p if and only if its symbol is invertible in Cp+H
p
.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 124–128, 1987.The authors are grateful to V. I. Vasyunin for assistance. 相似文献
11.
K. Retert 《Algebras and Representation Theory》2004,7(3):287-341
Noncommutative projective geometry studies noncommutative graded rings by replacing the variety by a suitable Grothendieck category. One way of studying the resulting category is to examine the full subcategories which behave like curves on a commutative variety. Smith and Zhang initiated such a study by considering the subcategory generated by a particular type of module they called a pure curve module in good position. This paper generalizes their construction by allowing more general modules. The resulting category is shown to be categorically equivalent to a quotient of the category of graded modules over a graded ring. In the course of defining the category equivalence, several dimensions, including projective, injective and Krull dimensions, are calculated. In particular, this extension allows examination of the category created from a line module over more general AS-regular rings than those considered by Smith and Zhang. For instance, suppose that C is a generic line module over R
d
, Stafford's Sklyanin-like algebra. Let C denote the category C generates. Then C is equivalent to the category of graded k[x, y]/(x
2 – y
2) modules under the Z × Z/2Z-grading where deg(x) = (–1, 0) and deg(y) = (–1,1). 相似文献
12.
F. M. Mukhamedov 《Mathematical Notes》2000,67(1):81-86
In this paper an analog of the Blum-Hanson theorem for quantum quadratic processes on the von Neumann algebra is proved, i.e.,
it is established that the following conditions are equivalent:
13.
O. I. Bogoyavlenskii 《Mathematical Notes》1970,8(1):514-517
It is proved that the property of a manifold Mn possessing a smooth function with given numbers of critical points of each index is homotopic invariant if Wh(
1 (Mn)) = 0 and every Z(
1 (Mn))-stable free module is free.Translated from Matematicheskie Zametki, Vol. 8, No. 1, pp. 77–83, July, 1970. 相似文献
14.
D. N. Ivanov 《Mathematical Notes》2005,77(1-2):194-198
It is proved that either a given balanced basis of the algebra (n + 1)M1 Mn or the corresponding complementary basis is of rank n + 1. This result enables us to claim that the algebra (n + 1)M1 Mn is balanced if and only if the matrix algebra Mn admits a WP-decomposition, i.e., a family of n + 1 subalgebras conjugate to the diagonal algebra and such that any two algebras in this family intersect orthogonally (with respect to the form tr XY) and their intersection is the trivial subalgebra. Thus, the problem of whether or not the algebra (n + 1)M1 Mn is balanced is equivalent to the well-known Winnie-the-Pooh problem on the existence of an orthogonal decomposition of a simple Lie algebra of type An–1 into the sum of Cartan subalgebras.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 213–218.Original Russian Text Copyright © 2005 by D. N. Ivanov.This revised version was published online in April 2005 with a corrected issue number. 相似文献
15.
16.
Let V be a compact complex analytic subset of a non-singular holomorphic manifold M. Assume that V has pure complex dimension n. Denote by V0 its regular part, and by [V] its fundamental class in H2n(V;
). If V is a locally complete intersection (LCI), it is known that the normal bundle NV_0 in M to V0 in M has a natural extension NV to all of V, so that we can define its Chern classes c(*)(NV) in cohomology, as well as the Chern classes cvir(*). If V is a locally complete intersection (LCI), it is known that the normal bundle NV_0 in M to V0 in M has a natural extension NV to all of V, so that we can define its Chern classes c(*)(NV) in cohomology, as well as the Chern classes cvir(*)
(V) of the virtual tangent bundle Tvir(V):=[TM|V - NV] in the K-theory K0(V). This has applications
17.
H
g Thi Nguyê 《Indagationes Mathematicae》2002,13(4):551-564
Let ω be a measure space and L∞ be the Banach algebra of all essentially bounded measurable scalar functions defined on ω. In the present paper we study so-called Banach M-spaces X such as Banach L∞-modules of
m-valued measurable functions in the vector-valued case m > 1. We present with complete proofs the new technical tool via so-called representative families (of m measurable functions) for X which is necessary for constructing correctly the theory of Banach M-spaces X of
m-valued functions with m > 1. We emphasize main new moments in proving basic theorems for Banach M-spaces of
m-valued functions with m > 1. 相似文献
18.
Thomas B. Dinsenbacher Douglas P. Hardin 《Journal of Fourier Analysis and Applications》1999,5(6):589-597
We give necessary and sufficient conditions for the existence and uniqueness of compactly supported distribution solutionsf=(f
1,...,f
r)T of nonhomogeneous refinement equations of the form
19.
A. N. Koryukin 《Algebra and Logic》1995,33(6):366-380
Suppose that H is a bialgebra over a field C and R = CV is the tensor algebra of the C-space V endowed with the structure of an H-module algebra, so that V is a submodule of the H-module R, RH is the algebra of H-invariants, and W, the support of the algebra RH, is the smallest subspace of the C-space V such that
. The main result of the paper is the theorem stating that if the algebra of H-invariants RH is finitely generated, then the support of RH is a finite-dimensional submodule of the H-module V, whose elements are H-semi-invariants of the same weight.Translated fromAlgebra i Logika, Vol. 33, No. 6, pp. 654–680, November–December, 1994.Supported by the Soros Foundation (grant RPS000) and the Russian Foundation for Fundamental Research (grant No. 93-01-16171). 相似文献
20.
A. V. Rukolaine 《Journal of Mathematical Sciences》1987,37(2):1023-1026
In the semigroup algebra A of a finite inverse semigroup S over the field of complex numbers to an indempotent e there is assigned the sum (e)=e+(–1)KeL1eiK, where ei,...,em are maximal preidempotents of the idempotent e, and the summation goes over all nonempty subsets {i1,...,ik} of the set {1,...m} Then for any class K of conjugate group elements of the semigroup S the element K=a·(a–1a) (the summation goes over all ag) is a central element of the algebra A, and the set {K} of all possible such elements is a basis for the center of the algebra A.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 74, pp. 154–158, 1978. 相似文献
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