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1.
2.
Let k be a field and E(n) be the 2
n+1-dimensional pointed Hopf algebra over k constructed by Beattie, Dăscălescu and Grünenfelder [J. Algebra, 2000, 225: 743–770]. E(n) is a triangular Hopf algebra with a family of triangular structures R
M
parameterized by symmetric matrices M in M
n
(k). In this paper, we study the Azumaya algebras in the braided monoidal category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
and obtain the structure theorems for Azumaya algebras in the category $
E_{(n)} \mathcal{M}^{R_M }
$
E_{(n)} \mathcal{M}^{R_M }
, where M is any symmetric n×n matrix over k. 相似文献
3.
P. A. Valinevih 《Journal of Mathematical Sciences》2010,168(6):811-819
We propose a method for construction of the general solution of the Yang–Baxter equation with the U
q
(sℓ
n
) symmetry algebra. This method is based on the factorization property of the corresponding L-operator. We present a closed-form expression for the universal R-matrix in the form of a difference operator acting on the
space of functions of n(n − 1) variables. Bibliography: 16 titles. 相似文献
4.
Let R be a ring, n a fixed nonnegative integer and FP
n
(F
n
) the class of all left (right) R-modules of FP-injective (flat) dimensions at most n. A left R-module M (resp., right R-module F) is called n-FI-injective (resp., n-FI-flat) if Ext
1(N,M) = 0 (resp., Tor
1(F,N) = 0) for any N ∈ FP
n
. It is shown that a left R-module M over any ring R is n-FI-injective if and only if M is a kernel of an FP
n
-precover f: A → B with A injective. For a left coherent ring R, it is proven that a finitely presented right R-module M is n-FI-flat if and only if M is a cokernel of an F
n
-preenvelope K → F of a right R-module K with F projective if and only if M ∈⊥
F
n
. These classes of modules are used to construct cotorsion theories and to characterize the global dimension of a ring. 相似文献
5.
Let D be an infinite division ring. A famous result due to Herstein says that every non-central element of D has infinitely many conjugates and so, if D
* is an FC-group, then D is a field. Let M be a maximal subgroup of GL
n
(D), where n ≥ 1. In this paper, we prove that if M is an FC-group, then it is the multiplicative group of some maximal subfield of M
n
(D). Moreover, if M is algebraic over Z(D), then [D : Z(D)] < ∞. 相似文献
6.
The j-function j(z) = q−1+ 744 + 196884q + ⋅s plays an important role in many problems. In [7], Zagier, presented an interesting series of functions obtained from the
j-function: jm(ζ) = (j(ζ) – 744)∨T0(m), where T0(m) is the usual m′th normalized weight 0 Hecke operator. In [3], Bruinier et al. show how this series of functions can be used to describe
all meromorphic modular forms on SL2(ℤ). In this note we use these functions and basic notions about modular forms to determine previously unidentified congruence
relations between the coefficients of Eisenstein series and the j-function.
2000 Mathematics Subject Classification: Primary–11B50, 11F03, 11F30
The author thanks the National Science Foundation for their generous support. 相似文献
7.
The lattice vertex operator algebra VL associated to a positive definite even lattice L has an automorphism of order 2 lifted from –1-isometry of L. The fixed point set VL+ of VL for the automorphism is naturally a vertex operator algebra. We prove that any 0-graded weak VL+-module is completely reducible.Supported by JSPS Research Fellowships for Young Scientists. 相似文献
8.
For a newform f for Γ0(N) of even weight k supersingular at a prime p ≥ 5, by using infinite dimensional p-adic analysis, we prove that the p-adic L-function L
p
(f,α; χ) has finite order of vanishing at any character of the form [(c)\tilde] s ( x ) = xs\tilde \chi _s \left( x \right) = x^s. In particular, under the natural embedding of ℤ
p
in the group of ℂ*
p
-valued continuous characters of ℤ*
p
, the order of vanishing at any point is finite. 相似文献
9.
Let M be a compact manifold of dimension n, P=P(h) a semiclassical pseudodifferential operator on M, and u=u(h) an L
2 normalized family of functions such that P(h)u(h) is O(h) in L
2(M) as h↓0. Let H⊂M be a compact submanifold of M. In a previous article, the second-named author proved estimates on the L
p
norms, p≥2, of u restricted to H, under the assumption that the u are semiclassically localized and under some natural structural assumptions about the principal symbol of P. These estimates are of the form Ch
−δ(n,k,p) where k=dim H (except for a logarithmic divergence in the case k=n−2, p=2). When H is a hypersurface, i.e., k=n−1, we have δ(n,n−1, 2)=1/4, which is sharp when M is the round n-sphere and H is an equator. 相似文献
10.
Behrooz Mirzaii 《Mathematische Annalen》2008,340(1):159-184
The homology of GL
n
(R) and SL
n
(R) is studied, where R is a commutative ‘ring with many units’. Our main theorem states that the natural map H
4(GL3(R), k) → H
4(GL4(R), k) is injective, where k is a field with char(k) ≠ 2, 3. For an algebraically closed field F, we prove a better result, namely, is injective. We will prove a similar result replacing GL by SL. This is used to investigate the indecomposable part of the
K-group K
4(R). 相似文献
11.
The article studies the cubic mapping graph Γ(n) of ℤ
n
[i], the ring of Gaussian integers modulo n. For each positive integer n > 1, the number of fixed points and the in-degree of the elements [`1]\overline 1 and [`0]\overline 0 in Γ(n) are found. Moreover, complete characterizations in terms of n are given in which Γ2(n) is semiregular, where Γ2(n) is induced by all the zero-divisors of ℤ
n
[i]. 相似文献
12.
In previous papers, we have constructed and studied mappings d
k
: M × M → ℝ called the H
k
-distance functions. The main result of this paper is a theorem on realizability of the generalized distances d
k
(υ, w), υ, w ∈ M, by critical values of the length functional L: Ω(M, υ, w) → ℝ generated by nontrivial homology classes of the space Ω(M, υ, w) of paths joining the points υ and w. 相似文献
13.
14.
In this paper, we give the eigenvalues of the manifold Sp(n)/U(n). We prove that an eigenvalue λ
s
(f
2, f
2, …, f
n
) of the Lie group Sp(n), corresponding to the representation with label (f
1, f
2, ..., f
n
), is an eigenvalue of the manifold Sp(n)/U(n), if and only if f
1, f
2, …, f
n
are all even. 相似文献
15.
In this work we generalize the case of scalar curvature zero the results of Simmons (Ann. Math. 88 (1968), 62–105) for minimal cones in Rn+1. If Mn−1 is a compact hypersurface of the sphere Sn(1) we represent by C(M)ε the truncated cone based on M with center at the origin. It is easy to see that M has zero scalar curvature if and only if the cone base on M also has zero scalar curvature. Hounie and Leite (J. Differential Geom. 41 (1995), 247–258) recently gave the conditions for the ellipticity of the partial differential equation of the scalar curvature.
To show that, we have to assume n ⩾ 4 and the three-curvature of M to be different from zero. For such cones, we prove that, for n ≤slant 7 there is an ε for which the truncate cone C(M)ε is not stable. We also show that for n ⩾ 8 there exist compact, orientable hypersurfaces Mn−1 of the sphere with zero scalar curvature and S3 different from zero, for which all truncated cones based on M are stable.
Mathematics Subject Classifications (2000): 53C42, 53C40, 49F10, 57R70. 相似文献
16.
J. Sunklodas 《Lithuanian Mathematical Journal》2005,45(4):475-486
We derive a lower bound of L
p
norms, 1 ⩽ p ⩽ ∞, in the central limit theorem for strongly mixing random variables X
1,..., X
n
with
under the boundedness condition ℙ{|X
i
| ⩽ M} = 1 with a nonrandom constantM > 0 and condition ∑
r⩾1
r
2α(r) < ∞, where α(r) are the Rosenblatt strong mixing coefficients.
__________
Translated from Lietuvos Matematikos Rinkinys, Vol. 45, No. 4, pp. 587–602, October–December, 2005. 相似文献
17.
V. E. Maiorov 《Ukrainian Mathematical Journal》2010,62(3):452-466
We study the approximation of the classes of functions by the manifold R
n
formed by all possible linear combinations of n ridge functions of the form r(a · x)): It is proved that, for any 1 ≤ q ≤ p ≤ ∞, the deviation of the Sobolev class W
r
p
from the set R
n
of ridge functions in the space L
q
(B
d
) satisfies the sharp order n
-r/(d-1). 相似文献
18.
Chun-Gil Park Hahng-Yun Chu Won-Gil Park Hee-Jeong Wee 《Czechoslovak Mathematical Journal》2005,55(4):1055-1065
It is shown that every almost linear Pexider mappings f, g, h from a unital C*-algebra
into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all unitaries u ∈
, all y ∈
, and all n ∈ ℤ, and that every almost linear continuous Pexider mappings f, g, h from a unital C*-algebra
of real rank zero into a unital C*-algebra ℬ are homomorphisms when f(2
n
uy) = f(2
n
u)f(y), g(2
n
uy) = g(2
n
u)g(y) and h(2
n
uy) = h(2
n
u)h(y) hold for all u ∈ {v ∈
: v = v* and v is invertible}, all y ∈
and all n ∈ ℤ.
Furthermore, we prove the Cauchy-Rassias stability of *-homomorphisms between unital C*-algebras, and ℂ-linear *-derivations on unital C*-algebras.
This work was supported by Korea Research Foundation Grant KRF-2003-042-C00008.
The second author was supported by the Brain Korea 21 Project in 2005. 相似文献
19.
Let M{\mathcal M} be a σ-finite von Neumann algebra and
\mathfrak A{\mathfrak A} a maximal subdiagonal algebra of M{\mathcal M} with respect to a faithful normal conditional expectation F{\Phi} . Based on Haagerup’s noncommutative L
p
space Lp(M){L^p(\mathcal M)} associated with M{\mathcal M} , we give a noncommutative version of H
p
space relative to
\mathfrak A{\mathfrak A} . If h
0 is the image of a faithful normal state j{\varphi} in L1(M){L^1(\mathcal M)} such that j°F = j{\varphi\circ \Phi=\varphi} , then it is shown that the closure of
{\mathfrak Ah0\frac1p}{\{\mathfrak Ah_0^{\frac1p}\}} in Lp(M){L^p(\mathcal M)} for 1 ≤ p < ∞ is independent of the choice of the state preserving F{\Phi} . Moreover, several characterizations for a subalgebra of the von Neumann algebra M{\mathcal M} to be a maximal subdiagonal algebra are given. 相似文献
20.
Lingli Wang 《Frontiers of Mathematics in China》2010,5(1):179-190
Let G be a finite group, and let π
e
(G) be the spectrum of G, that is, the set of all element orders of G. In 1987, Shi Wujie put forward the following conjecture. If G is a finite group and M is a non-abelian simple group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M). In this short paper, we prove that if G is a finite group, then G ≅ M if and only if |G| = |M| and π
e
(G) = π
e
(M), where M = D
n
(2) and n is even. 相似文献