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1.
Let A≡KΔ /I be a factor of a path algebra. We develop a strategy to compute dim H
1(A), the dimension of the first Hochschild cohomology group of A, using combinatorial data from (Δ,I). That allows us to connect dim H
1(A) with the rank and p-rank of the fundamental group π1(Δ,I) of (Δ,I). We get explicit formulae for dim H
1(A), when every path in Δ parallel to an arrow belongs to I or when I is homogeneous.
Received: 12 April 1999 / Revised version: 9 October 2000 相似文献
2.
Let A be a commutative integral domain that is a finitely generated algebra over a field k of characteristic 0 and let ø be a k-algebra automorphism of A of finite order m. In this note we study the ring D(A;ø of differential operators introduced by A.D. Bell. We prove that if A is a free module over the fixed sub-ring A ø, with a basis containing 1, then D(A;ø) is isomorphic to the matrix ring Mm(D(A ø). It follows from Grothendieck's Generic Flatness Theorem that for an arbitrary A there is an element c?Asuch that D(A[c-1];ø)?M m(D(A[c-1]ø)). As an application, we consider the structure of D(A;ø)when A is a polynomial or Laurent polynomial ring over k and ø is a diagonalizable linear automorphism. 相似文献
3.
D. M. Riley proved in [3] that, if A and
B are either Lie nilpotent or Lie metabelian algebras, then their tensor product A ⊗ B is Lie soluble and obtained bounds on the Lie derived length of A ⊗ B. The aim of the present note is to improve Riley’s bounds; moreover we consider also the cases in which A and B are either strongly Lie soluble or strongly Lie nilpotent algebras.
Received: 5 April 2006
The first two authors partially supported by MIUR-Italy via PRIN “Group theory and applications”. 相似文献
4.
Subhash J. Bhatt 《Proceedings Mathematical Sciences》2006,116(2):161-173
Given anm-tempered strongly continuous action α of ℝ by continuous*-automorphisms of a Frechet*-algebraA, it is shown that the enveloping ↡-C
*-algebraE(S(ℝ, A∞, α)) of the smooth Schwartz crossed productS(ℝ,A
∞, α) of the Frechet algebra A∞ of C∞-elements ofA is isomorphic to the Σ-C
*-crossed productC
*(ℝ,E(A), α) of the enveloping Σ-C
*-algebraE(A) ofA by the induced action. WhenA is a hermitianQ-algebra, one getsK-theory isomorphismRK
*(S(ℝ, A∞, α)) =K
*(C
*(ℝ,E(A), α) for the representableK-theory of Frechet algebras. An application to the differential structure of aC
*-algebra defined by densely defined differential seminorms is given. 相似文献
5.
Nathan S. Feldman 《Integral Equations and Operator Theory》2007,58(2):153-173
A pair of commuting operators, (A,B), on a Hilbert space
is said to be hypercyclic if there exists a vector
such that {A
n
B
k
x : n, k ≥ 0} is dense in
. If f, g ∈H
∞(G) where G is an open set with finitely many components in the complex plane, then we show that the pair (M
*
f
, M
*
g
) of adjoints of multiplcation operators on a Hilbert space of analytic functions on G is hypercyclic if and only if the semigroup they generate contains a hypercyclic operator. However, if G has infinitely many components, then we show that there exists f, g ∈H
∞(G) such that the pair (M
*
f
, M
*
g
) is hypercyclic but the semigroup they generate does not contain a hypercyclic operator. We also consider hypercyclic n-tuples. 相似文献
6.
7.
Manfred Knebusch 《Positivity》2007,11(4):639-686
Given a commutative ring A equipped with a preordering A+ (in the most general sense, see below), we look for a fractional ring extension (= “ring of quotients” in the sense of Lambek
et al. [L]) as big as possible such that A+ extends to a preordering R+ of R (i.e. with A ∩ R+ = A+) in a natural way. We then ask for subextensions A ⊂ B of A ⊂ R such that A is convex in B with respect to B+ : = B ∩ R+.
Supported by DFG.
A short form of this article has been delivered at the conference Carthapos 2006 at Carthago (Tunisia). 相似文献
8.
Let −A be a linear, injective operator, on a Banach spaceX. We show that ∃ anH
∞ functional calculus forA if and only if −A generates a bouned strongly continuous holomorphic semigroup of uniform weak bounded variation, if and only ifA(ζ+A)
−1 is of uniform weak bounded variation. This provides a sufficient condition for the imaginary powers ofA, {A−is} sεR, to extend to a strongly continuous group of bounded operators; we also give similar necessary conditions. 相似文献
9.
ZhiXiangWU 《数学学报(英文版)》2004,20(1):125-134
In this paper.we study the ring #(D.B)and obtain two very interesting results. First we prove in Theorem 3 that the category of rational left BU-modules is equivalent to both the category of #-rational left modules and the category of all(B.D)-Hopf modules BM^D.Cai and Chen have proved this result in the case B=D=A.Secondly they have proved that if A has a nonzero left integral then A#A^*rat is a dense subring of Endk(A).We prove that #(A,A) is a dense subring of Endk(Q),where Q is a certain subspace of #(A.A)under the condition that the antipode is bijective(see Theorem18).This condition is weaker than the condition that A has a nonzero integral.It is well known the antipode is bijective in case A has a nonzero integral.Furthermore if A has nonzero left integral,Q can be chosen to be A(see Corollary 19)and #(A,A)is both left and right primitive.Thus A#A^*rat #(A,A)-Endk(A).Moreover we prove that the left singular ideal of the ring #(A,A)is zero.A corollary of this is a criterion for A with nonzero left integral to be finite-dimensional,namely the ring #(A,A)has a finite uniform dimension. 相似文献
10.
We study the filter ℒ*(A) of computably enumerable supersets (modulo finite sets) of an r-maximal set A and show that, for some such set A, the property of being cofinite in ℒ*(A) is still Σ0
3-complete. This implies that for this A, there is no uniformly computably enumerable “tower” of sets exhausting exactly the coinfinite sets in ℒ*(A).
Received: 6 November 1999 / Revised version: 10 March 2000 /?Published online: 18 May 2001 相似文献
11.
三幂等符号模式矩阵的结构 总被引:2,自引:0,他引:2
Abstract. A matrix whose entries are , -, and 0 is called a sign pattern matrix. For a signpattern matrix A,if A3 =A, then A is said to be sign tripotent. In this paper, the characteriza-tion of the n by n(n≥2) sign pattern matrices A which are sign tripotent has been given out.Furthermore, the necessary and sufficient condition of A3=A but A2≠A is obtained, too. 相似文献
12.
It is shown that ifA andB are non-empty subsets of {0, 1}
n
(for somenεN) then |A+B|≧(|A||B|)α where α=(1/2) log2 3 here and in what follows. In particular if |A|=2
n-1 then |A+A|≧3
n-1 which anwers a question of Brown and Moran. It is also shown that if |A| = 2
n-1 then |A+A|=3
n-1 if and only if the points ofA lie on a hyperplane inn-dimensions. Necessary and sufficient conditions are also given for |A +B|=(|A||B|)α. The above results imply the following improvement of a result of Talagrand [7]: ifX andY are compact subsets ofK (the Cantor set) withm(X),m(Y)>0 then λ(X+Y)≧2(m(X)m(Y))α wherem is the usual measure onK and λ is Lebesgue measure. This also answers a question of Moran (in more precise terms) showing thatm is not concentrated on any proper Raikov system. 相似文献
13.
We prove that, ifA is a complex Banach algebra with a unit 1 and a conjugate-linear vector space involution* such that 1*=1 and‖a
*a‖=‖a*‖ ‖a‖ for alla inA, and ifdim(A)≥3, thenA is a C*-algebra. The two-dimensional case is also considered and described. 相似文献
14.
We introduce a simultaneous decomposition for a matrix triplet (A,B,C
∗), where A=±A
∗ and (⋅)∗ denotes the conjugate transpose of a matrix, and use the simultaneous decomposition to solve some conjectures on the maximal
and minimal values of the ranks of the matrix expressions A−BXC±(BXC)∗ with respect to a variable matrix X. In addition, we give some explicit formulas for the maximal and minimal values of the inertia of the matrix expression A−BXC−(BXC)∗ with respect to X. As applications, we derive the extremal ranks and inertias of the matrix expression D−CXC
∗ subject to Hermitian solutions of a consistent matrix equation AXA
∗=B, as well as the extremal ranks and inertias of the Hermitian Schur complement D−B
∗
A
∼
B with respect to a Hermitian generalized inverse A
∼ of A. Various consequences of these extremal ranks and inertias are also presented in the paper. 相似文献
15.
A. J. Hoffman 《Israel Journal of Mathematics》1974,17(1):69-75
To every symmetric matrixA with entries ±1, we associate a graph G(A), and ask (for two different definitions of distance) for the distance ofG(A) to the nearest complete bipartite graph (cbg). Letλ
1(A),λ
1 (A) be respectively the algebraically largest and least eigenvalues ofA. The Frobenius distance (see Section 4) to the nearest cbg is bounded above and below by functions ofn −λ
1 (A), wheren=ord A. The ordinary distance (see Section 1) to the nearest cbg is shown to be bounded above and below by functions ofλ
1 (A). A curious corollary is: there exists a functionf (independent ofn, and given by (1.1)), such that |λ
i
(A) | ≦f(λ
1(A), whereλ
i
(A) is any eigenvalue ofA other thanλ
i
(A).
This work was supported (in part) by the U.S. Army under contract #DAHC04-C-0023. 相似文献
16.
Milan Jasem 《Mathematica Slovaca》2011,61(5):827-833
Let A = (A,⊕,−,∼, 0, 1) be a GMV-algebra and ρ: A × A → A the distance function on A defined by ρ(x, y) = (x∨y)−(x∧y) for each x, y ∈ A. 相似文献
17.
We callE ⊆ {0,1}
k
projective if for some countableA ⊆κ there is anE
A
⊆ {0, 1}
A
such thatE=E
A
×{0,1}
k\A
andE
A
is a projective subset of the Cantor set {0, 1}
A
. We construct a model where Haar measure on {0,1}
k
has no projective lifting (and in particular no Baire lifting) for anyκ≥ω.
Research partially supported by NATO Science Fellowship. The first author would like to thank the Mathematics Department at
the University of Essex for its hospitality during the academic year 1988/89 while part of this research was being carried
out.
This research was initiated while the second author was a postdoctoral fellow at the University of Toronto. Its completion
was supported by NSF grant DMS-8505550. 相似文献
18.
We show that for every ɛ > 0 there is a set A ⊂ ℝ3 such that H
1 ⌞A is a monotone measure, the corresponding tangent measures at the origin are non-conical and non-unique and H
1 ⌞A has the 1-dimensional density between 1 and 2+ɛ everywhere in the support. 相似文献
19.
It is known that any strict tensor category (C⊗I) determines a braided tensor categoryZ(C), the centre ofC. WhenA is a finite dimension Hopf algebra, Drinfel’d has proved thatZ(A
M) is equivalent to
D(A)
M as a braided tensor category, whereA
M is the left A-module category andD(A) is the Drinfel’d double ofA. For a braided tensor category, the braidC
U,v is a natural isomorphism for any pair of object (U,V) in. If weakening the natural isomorphism of the braidC
U,V to a natural transformation, thenC
U,V is a prebraid and the category with a prebraid is called a prebraided tensor category. Similarly it can be proved that any strict
tensor category determines a prebraided tensor category Z∼ (C), the near centre of. An interesting prebraided tensor structure of the Yetter-Drinfel’d category
C*A
YD
C*A
given, whereC # A is the smash product bialgebra ofC andA. And it is proved that the near centre of Doi-Hopf module
A
M(H)
C
is equivalent to the Yetter-Drinfel’ d
C*A
YD
C*A
as prebraided tensor categories. As corollaries, the prebraided tensor structures of the Yetter-Drinfel’d category
A
YD
A
, the centres of module category and comodule category are given. 相似文献
20.
The paper aims at developing a theory of nuclear (in the topological algebraic sense) pro-C*-algebras (which are inverse limits of C*-algebras) by investigating completely positive maps and tensor products. By using the structure of matrix algebras over a
pro-C*-algebra, it is shown that a unital continuous linear map between pro-C*-algebrasA andB is completely positive iff by restriction, it defines a completely positive map between the C*-algebrasb(A) andb(B) consisting of all bounded elements ofA andB. In the metrizable case,A andB are homeomorphically isomorphic iff they are matricially order isomorphic. The injective pro-C*-topology α and the projective pro-C*-topology v on A⊗B are shown to be minimal and maximal pro-C*-topologies; and α coincides with the topology of biequicontinous convergence iff eitherA orB is abelian. A nuclear pro-C*-algebraA is one that satisfies, for any pro-C*-algebra (or a C*-algebra)B, any of the equivalent requirements; (i) α =v onA ⊗B (ii)A is inverse limit of nuclear C*-algebras (iii) there is only one admissible pro-C*-topologyon A⊗B (iv) the bounded partb(A) ofA is a nuclear C⊗-algebra (v) any continuous complete state map A→B* can be approximated in simple weak* convergence by certain finite rank complete state maps. This is used to investigate permanence properties of nuclear pro-C*-algebras pertaining to subalgebras, quotients and projective and inductive limits. A nuclearity criterion for multiplier
algebras (in particular, the multiplier algebra of Pedersen ideal of a C*-algebra) is developed and the connection of this C*-algebraic nuclearity with Grothendieck’s linear topological nuclearity is examined. A σ-C*-algebraA is a nuclear space iff it is an inverse limit of finite dimensional C*-algebras; and if abelian, thenA is isomorphic to the algebra (pointwise operations) of all scalar sequences. 相似文献