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Cn(R)表示交换环R上n阶循环矩阵的全体.根据通常矩阵的乘法·和加法,Cn(R)同构于一个箭图代数.考虑矩阵的Hadamard积o,Cn(R)也为结合代数,在Cn(R)上定义了新的余乘△,余单位ε和对极S使得(Cn(R),o,μ,Δ,ε,S)做成Hopf代数. 相似文献
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《数学的实践与认识》2019,(23)
令R是特征为2,且含有非平凡幂等元与单位元的素环.假设f:R→R是满射,k=2,3.证明了,f满足[f(x),f(y)]_k=[x,y]_k=[[x,y]_(k-1),y]对所有元x,y∈R成立当且仅当存在映射μ:R→C和元λ∈C使得f(x)=λx+μ(x)对所有元x∈R成立,其中λ~(k+1)=1,C是R的扩展中心. 相似文献
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从对称矩阵代数到全矩阵代数的线性群逆保持 总被引:1,自引:0,他引:1
设F是一个特征不为2的域,Mn(F)和Sn(F)分别记F上的n×n全矩阵代数和对称矩阵代数.所有的从Sn(F)到Mn(F)的保群逆的线性映射被刻划,作为一个中间步骤,三个矩阵的同时相似标准形也被证明.这个标准形简化了从Sn(F)到Mn(F)的保群逆的线性映射的刻划. 相似文献
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奇异H-矩阵并行算法 总被引:2,自引:0,他引:2
1 引 言对于H矩阵类,到目前为止,人们关注的是非奇异H矩阵,对于奇异H矩阵研究结果很少,不象奇异M-矩阵研究的丰富[1-4]及获得了半收敛的一些结论,王川龙和游兆永将并行算法用于奇异M矩阵[5].本文的目的就是将并行算法用于奇异H矩阵.为此,首先讨论了奇异H矩阵与奇异M矩阵的关系.2 符号特征设Mn(R)代表实方阵的全体,A∈Mn(R),不特殊说明,A=D-B表示Jacobi分裂,〈A〉是A的比较矩阵,detA表示A的行列式,ρ(A)表示A的谱半径,μ(A)表示A的谱〈n〉={1,2,…,n},A[α|α]表示由α所决定的主子矩阵,α∈〈n〉.定理2.1[8] 设A是实H矩阵… 相似文献
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设$F$ 为域, $n\geq 3$, $\bf{N}$$(n,\mathbb{F})$ 为域$\mathbb{F}$ 上所有$n\times n$ 阶严格上三角矩阵构成的严格上三角矩阵李代数, 其李运算为$[x,y]=xy-yx$. $\bf{N}$$(n, \mathbb{F})$ 上一线性映射$\varphi$ 称为积零导子,如果由$[x,y]=0, x,y\in \bf{N}$$(n,\mathbb{F})$,总可推出 $[\varphi(x), y]+[x,\varphi(y)]=0$. 本文证明 $\bf{N}$$(n,\mathbb{F})$上一线性映射 $\varphi$ 为积零导子当且仅当 $\varphi$ 为$\bf{N}$$(n,\mathbb{F})$ 上内导子, 对角线导子, 极端导子, 中心导子和标量乘法的和. 相似文献
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Let G be a group and assume that (A
p
)
p∈G
is a family of algebras with identity. We have a Hopf G-coalgebra (in the sense of Turaev) if, for each pair p,q ∈ G, there is given a unital homomorphism Δ
p,q
: A
pq
→ A
p
⊗ A
q
satisfying certain properties. Consider now the direct sum A of these algebras. It is an algebra, without identity, except when G is a finite group, but the product is non-degenerate. The maps Δ
p,q
can be used to define a coproduct Δ on A and the conditions imposed on these maps give that (A,Δ) is a multiplier Hopf algebra. It is G-cograded as explained in this paper. We study these so-called group-cograded multiplier Hopf algebras. They are, as explained above, more general than the Hopf group-coalgebras as introduced by Turaev. Moreover, our point of
view makes it possible to use results and techniques from the theory of multiplier Hopf algebras in the study of Hopf group-coalgebras
(and generalizations). In a separate paper, we treat the quantum double in this context and we recover, in a simple and natural
way (and generalize) results obtained by Zunino. In this paper, we study integrals, in general and in the case where the components
are finite-dimensional. Using these ideas, we obtain most of the results of Virelizier on this subject and consider them in
the framework of multiplier Hopf algebras.
Presented by Ken Goodearl. 相似文献
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Let 𝔄 denote the C*-algebra of bounded operators on L
2 ℝ generated by: (i) all multiplications a(M) by functions a∈C[ − ∞, + ∞], (ii) all multiplications by 2π-periodic continuous functions, and (iii) all operator of the form F
−1
b(M)F, where F denotes the Fourier transform and b∈C[ − ∞, + ∞]. A given A ∈ 𝔄 is a Fredholm operator if and only if σ(A) and γ(A) are invertible, where σ denotes the continuous extension of the usual principal symbol, while γ denotes an operator-valued “boundary principal symbol” (the “boundary” here consists of two copies of the circle, one at
each end of the real line). We give two proofs of the fact that K
0(𝔄) is isomorphic to ℤ and that K
1(𝔄) is isomorphic to ℤ ⊕ ℤ . We do it first by computing the connecting mappings in the six-term exact sequence associated
to σ. For the second proof, we show that the image of γ is isomorphic to the direct sum of two copies of the crossed product
, where α denotes the translation-by-one automorphism. Its K-theory can be computed using the Pimsner–Voiculescu exact sequence,
and that information suffices for the analysis of the standard cyclic exact sequence associated to γ.
Received: February 2006 相似文献
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We investigate various number system constructions. After summarizing earlier results we prove that for a given lattice Λ
and expansive matrix M: Λ → Λ if ρ(M
−1) < 1/2 then there always exists a suitable digit set D for which (Λ, M, D) is a number system. Here ρ means the spectral radius of M
−1. We shall prove further that if the polynomial f(x) = c
0 + c
1
x + ··· + c
k
x
k
∈ Z[x], c
k
= 1 satisfies the condition |c
0| > 2 Σ
i=1
k
|c
i
| then there is a suitable digit set D for which (Z
k
, M, D) is a number system, where M is the companion matrix of f(x).
The research was supported by OTKA-T043657 and Bolyai Fellowship Committee. 相似文献
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We characterize the surjective additive maps compressing the spectral function Δ(·) between standard operator algebras acting on complex Banach spaces, where Δ(·) stands for any one of nine spectral functions σ(·), σl(·), σr(·),σl(·) ∩ σr(·), δσ(·), ησ(·), σap(·), σs(·), and σap(·) ∩ σs(·). 相似文献
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The Dunford-Pettis property in Jb*-Triples 总被引:2,自引:0,他引:2
JB*-triples occur in the study of bounded symmetric domainsin several complex variables and in the study of contractiveprojections on C*-algebras. These spaces are equipped with aternary product {·,·,·}, the Jordan tripleproduct, and are essentially geometric objects in that the linearisometries between them are exactly the linear bijections preservingthe Jordan triple product (cf. [23]). 相似文献
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Fengwei Zhong Huafei Sun Zhenning Zhang 《Bulletin of the Brazilian Mathematical Society》2008,39(1):1-10
In this paper, we consider the problem of distribution control from the viewpoint of information geometry. Different from
most existing models used in stochastic control, it is assumed that the control input directly affects the distribution of
the system output in probability sense. Here, we set up a new manifold (S), meanwhile the B-spline manifold (B) and the system output manifold (M) can be referred to as its submanifolds. We give an information geometrical algorithm which can be called as geodesic-projection
algorithm using the properties of manifold. In the geodesic step, we can obtain the geodesic equation from the initial point
V0 = (ω10, ω20, ··· , ω(n−1)0) to the specified point Vg = (ω1g, ω2g, ··· , ω(n−1)g) in B. This gives us an optimal trajectory for the points changing along in B. In the projection step, we project the sample points selected from the geodesic onto M. The coordinates of the projections in M give the trajectory of the control input u. 相似文献
20.
We continue the study of quantum matrix algebras of the GL(m|n) type. We find three alternative forms of the Cayley-Hamilton identity; most importantly, this identity can be represented
in a factored form. The factorization allows naturally dividing the spectrum of a quantum supermatrix into subsets of “even”
and “odd” eigenvalues. This division leads to a parameterization of the characteristic subalgebra (the subalgebra of spectral
invariants) in terms of supersymmetric polynomials in the eigenvalues of the quantum matrix. Our construction is based on
two auxiliary results, which are independently interesting. First, we derive the multiplication rule for Schur functions s
λ
(M) that form a linear basis of the characteristic subalgebra of a Hecke-type quantum matrix algebra; the structure constants
in this basis coincide with the Littlewood-Richardson coefficients. Second, we prove a number of bilinear relations in the
graded ring Λ of symmetric functions of countably many variables.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 1, pp. 14–46, April, 2006. 相似文献