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1.
Bang-Yen Chen 《Annals of Global Analysis and Geometry》1994,12(1):87-96
In the first part of this series, we prove that the tensor product immersionf
1
f
2k
of2k isometric spherical immersions of a Riemannian manifoldM in Euclidean space is of-type with k and classify tensor product immersionsf
1
f
2k
which are ofk-type. In this article we investigate the tensor product immersionsf
1
f
2k
which are of (k+1)-type. Several classification theorems are obtained. 相似文献
2.
Antonio Lanteri 《Monatshefte für Mathematik》1990,109(1):69-77
LetX be a complex connected projective smooth algebraic surface and letL be an ample line bundle onX. The maps associated with the pluriadjoint bundles (K
X
L) 1,t2, are studied by combining an ampleness result forK
X
L with a very recent result by Reider. It turns out that apart from some exceptions and up to reductions, 1) (K
X
L)3 is very ample; 2) (K
X
L) 2 is ample and spanned by global sections and is very ample unless eitherg (L)=2 (arithmetic genus ofL) orX contains an elliptic curveE withE
2=0,E·L=1;3) when (K
X
L) 2 is not very ample, the associated map has degree 4, equality implying thatg (L)=2 and
. 相似文献
3.
In this paper we first show that if X is a Banach space and is a left invariant crossnorm on lX, then there is a Banach lattice L and an isometric embedding J of X into L, so that I J becomes an isometry of lX onto lm J(X). Here I denotes the identity operator on l and lm J(X) the canonical lattice tensor product. This result is originally due to G. Pisier (unpublished), but our proof is different. We then use this to prove the main results which characterize the Gordon–Lewis property GL and related structures in terms of embeddings into Banach lattices. 相似文献
4.
R. Zekri 《K-Theory》1990,3(6):543-559
We show that the universalC*-algebras KqA and K2A are homotopy equivalent and define abstract analogues of the Bott elements inKK-theory. 相似文献
5.
In this paper we show that over any field K of characteristic different from 2, the Maslov index gives rise to a 2-cocycle on the stable symplectic group with values in the Witt group. We also show that this cocycle admits a natural reduction to I
2(K) and that the induced natural homomorphism from K
2
Sp(K)I
2(K) is indeed the homomorphism given by the symplectic symbol {x, y} mapping to the Pfister form 1, -x 1, –y. 相似文献
6.
The Long Dimodules Category and Nonlinear Equations 总被引:2,自引:0,他引:2
G. Militaru 《Algebras and Representation Theory》1999,2(2):177-200
Let H be a bialgebra and H LH be the category of Long H-dimodules defined, for a commutative and co-commutative H, by F. W. Long and studied in connection with the Brauer group of a so-called H-dimodule algebra. For a commutative and co-commutative H, H LH =H YDH (the category of Yetter–Drinfel'd modules), but for an arbitrary H, the categories H LH and H YDH are basically different. Keeping in mind that the category H YDH is deeply involved in solving the quantum Yang–Baxter equation, we study the category H LH of H-dimodules in connection with what we have called the D-equation: R12 R23 = R23 R12, where R Endk(M M) for a vector space M over a field k. The main result is a FRT-type theorem: if M is finite-dimensional, then any solution R of the D-equation has the form R = R(M, , ), where (M, , ) is a Long D(R)-dimodule over a bialgebra D(R) and R(M, , ) is the special map R(M, , )(m n) : = n1 m n0. In the last section, if C is a coalgebra and I is a coideal of C, we introduce the notion of D-map on C, that is a k-bilinear map : C C / I k satisfying a condition which ensures on the one hand that, for any right C-comodule, the special map R is a solution of the D-equation and, on the other, that, in the finite case, any solution of the D-equation has this form. 相似文献
7.
Summary The notion of a quantum Poisson process over a quantum measure space is introduced. This process is used to construct new quantum Markov processes on the matrix algebraM
n
with stationary faithful state . If (, ) is the quantum measure space in question ( a von Neumann algebra and a faithful normal weight), then the semigroupe
tL
of transition operators on (M
n
, ) has generator whereu is an arbitrary unitary element of the centraliser of (M
n
,).Supported by the Netherlands Organization for Scientific Research NWO 相似文献
8.
The non-commutative torus C
*(n,) is realized as the C*-algebra of sections of a locally trivial C*-algebra bundle over S with fibres isomorphic to C
*n/S, 1) for a totally skew multiplier 1 on n/S. D. Poguntke [9] proved that A
is stably isomorphic to C(S) C(*( Zn/S, 1) C(S) A Mkl( C) for a simple non-commutative torus A and an integer kl. It is well-known that a stable isomorphism of two separable C*-algebras is equivalent to the existence of equivalence bimodule between them. We construct an A-C(S) A-equivalence bimodule. 相似文献
9.
Siegfried Steiner 《manuscripta mathematica》1977,20(3):277-300
Let E be a n-dimensional euclidean vector space. The subset V
k
n
={x ... x | x E} of kE is called a Veronesemanifold. The scalar product of E induces a euclidean structure on kE. Passing to the corresponding projective space
, one may consider
as a riemannian submanifold of the space form
. In this paper we study properties of the pair
of riemannian manifolds. 相似文献
10.
Let be a G-symmetric graph whose vertex set admits a nontrivial G-invariant partition with block size v. Let
be the quotient graph of relative to and [B,C] the bipartite subgraph of induced by adjacent blocks B,C of . In this paper we study such graphs for which
is connected, (G, 2)-arc transitive and is almost covered by in the sense that [B,C] is a matching of v-1 2 edges. Such graphs arose as a natural extremal case in a previous study by the author with Li and Praeger. The case
K
v+1 is covered by results of Gardiner and Praeger. We consider here the general case where
K
v+1, and prove that, for some even integer n 4,
is a near n-gonal graph with respect to a certain G-orbit on n-cycles of
. Moreover, we prove that every (G, 2)-arc transitive near n-gonal graph with respect to a G-orbit on n-cycles arises as a quotient
of a graph with these properties. (A near n-gonal graph is a connected graph of girth at least 4 together with a set of n-cycles of such that each 2-arc of is contained in a unique member of .) 相似文献
11.
S. Caenepeel Bogdan Ion G. Militaru Shenglin Zhu 《Algebras and Representation Theory》2000,3(1):19-42
We consider the factorization problem for bialgebras. Let L and H be algebras and coalgebras (but not necessarily bialgebras) and consider two maps R : H L L H and W : L H H L. We introduce a product K = L
W
R
H and we give necessary and sufficient conditions for K to be a bialgebra. Our construction generalizes products introduced by Majid and Radford. Also, some of the pointed Hopf algebras that were recently constructed by Beattie, Dsclescu and Grünenfelder appear as special cases. 相似文献
12.
P. Lancaster 《Numerische Mathematik》1972,19(3):206-208
Summary IfX is a finite-dimensional linear space andL(X) the linear space of linear operators onX thenL(X) may be represented asXX
*. IfE={e
1, ...,e
n
} is a basis forX and e
j
y
j
*
is a typical element ofXX
*, then norms can be introduced onL(X) in the form y
j
*
e
j
. Given that the norm onX isE-absolute we derive a necessary and sufficient condition for the norm onL(X) to be submultiplicative. 相似文献
13.
LetA be a von Neumann algebra and a faithful normal state. ThenO
= {
ºAd(g
1) :g G
A
}andU
= {
ºAd(u
*) :u U
A
are homogeneous reductive spaces. IfA is aC
* algebra,e
the Jones projection of the faithful state viewed as a conditional expectation, then we prove that the similarity orbit ofe
by invertible elements ofA can be imbedded inAA in such a way thate
is carried to 1 1 and the orbit ofe
to a homogeneous reductive space and an analytic submanifold ofAA. 相似文献
14.
Erik Valtonen 《manuscripta mathematica》1989,63(1):45-68
LetR be a commutative ring with 1 andM anR-module. If:M
R
MR is anR-module homomorphism satisfying(mm)=(mm) and(mm)m=m(mm), the additive abelian groupRM becomes a commutative ring, if multiplication is defined by (r,m)(r,m)=(rr+(mm),rm+rm). This ring is called the semitrivial extension ofR byM and and it is denoted byR
M. This generalizes the notion of a trivial extension and leads to a more interesting variety of examples. The purpose of this paper is to studyR
M; in particular, we are interested in some homological properties ofR
M as that of being Cohen-Macaulay, Gorenstein or regular. A sample result: Let (R,m) be a local Noetherian ring,M a finitely generatedR-module and Im() m. ThenR
M is Gorenstein if and only if eitherRM is Gorenstein orR is Gorenstein,M is a maximal Cohen-Macaulay module andMM
*, where the isomorphism is given by the adjoint of. 相似文献
15.
Andrew Ranicki 《K-Theory》1987,1(2):115-170
The algebraic K-theory product K
0(A) K
1
B K
1(A B) for rings A, B is given a chain complex interpretation, using the absolute torsion invariant introduced in Part I. Given a finitely dominated A-module chain complex C and a round finite B-module chain complex D, it is shown that the A B-module chain complex C D has a round finite chain homotopy structure. Thus, if X is a finitely dominated CW complex and Y is a round finite CW complex, the product X × Y is a CW complex with a round finite homotopy structure. 相似文献
16.
R. A. Cuninghame-Green 《Mathematical Programming》1976,10(1):111-123
An axiomatic theory of linear operators can be constructed for abstract spaces defined over (R, , ), that is over the (extended) real numbersR with the binary operationsx y = max (x,y) andx y = x + y. Many of the features of conventional linear operator theory can be reproduced in this theory, although the proof techniques are quite different. Specialisation of the theory to spaces ofn-tuples provides techniques for analysing a number of well-known operational research problems, whilst specialisation to function spaces provides a natural formal framework for certain familiar problems of approximation, optimisation and duality. 相似文献
17.
Teodor Banica 《Integral Equations and Operator Theory》2001,39(1):1-14
We construct inclusions of the form (B
0P)
G
(B
1P)
G
, whereG is a compact quantum group of Kac type acting on an inclusion of finite dimensional C*-algebrasB
0B
1 and on aII
1 factorP. Under suitable assumptions on the actions ofG, this is a subfactor, whose Jones tower and standard invariant can be computed by using techniques of A. Wassermann. The subfactors associated to subgroups of compact groups, to projective representations of compact groups, to finite quantum groups, to finitely generated discrete groups, to vertex models and to spin models are of this form. 相似文献
18.
M. Guyot 《Mathematische Annalen》1985,270(1):47-62
Conclusion SoitE un fibré uniforme surG(d,n). Nous avons étudié exhaustivement les cas où rangEd. montrant queE est soit somme directe de fibrés ou droites, soit, sir=d, indécomposable et isomorphe àH
d
O
G
() où àH
d
*
O
G
().Si rangE=(n-d), nous avons étudié les cas oùE est décomposable en fibrés en droites ou indécomposable et isomorphe àQ
n d
O
G
() où àQ
n
*
d
O
G
(). L'étude des fibrés indécomposables de rangd, et (n-d) nous a montré que les quatre fibrés universels surG(d,n), sont caractérisés par leur rang, leur polynôme de Chern et al propriété d'uniformité. 相似文献
19.
In this article the topologically exact sequences
of locally convex spaces are characterized for which for every locally convex space F the map id : FE F Q is a homomorphism, or equivalently, the map id L : FK F E is a topological injection. This is motivated by the problem of lifting Q-valued functions with certain given properties to E-valued functions with the same or slightly weaker properties, which may also be considered as the investigation of parameter dependences of solutions of linear (differential) equations. Applications to partial differential equations and to Fredholm functions are given. 相似文献
20.
Micheline Vigué-Poirrier 《manuscripta mathematica》1986,56(2):177-191
Let X be a nilpotent space such that it exists k1 with Hp (X,) = 0 p > k and Hk (X,) 0, let Y be a (m–1)-connected space with mk+2, then the rational homotopy Lie algebra of YX (resp.
is isomorphic as Lie algebra, to H* (X,) (* (Y) ) (resp.+ (X,) (* (Y) )). If X is formal and Y -formal, then the spaces YX and
are -formal. Furthermore, if dim * (Y) is infinite and dim H* (Y,Q) is finite, then the sequence of Betti numbers of
grows exponentially. 相似文献