共查询到20条相似文献,搜索用时 31 毫秒
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.
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 This result is originally due to G. Pisier (unpublished), but our proof is different.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
3.
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
4.
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
5.
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
6.
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
7.
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
8.
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
9.
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
10.
Horst Elmar Winkelnkemper 《Annals of Global Analysis and Geometry》1992,10(3):209-218
Let
t
be the flow (parametrized with respect to arc length) of a smooth unit vector field v on a closed Riemannian manifold M
n
, whose orbits are geodesics. Then the (n-1)-plane field normal to v, v, is invariant under d
t
and, for each x M, we define a smooth real function
x
(t) : (1 +
i
(t)), where the i(t) are the eigenvalues of AA
T, A being the matrix (with respect to orthonormal bases) of the non-singular linear map d2t
, restricted to v at the point x
-t M
n.Among other things, we prove the
Theorem (Theorem II, below). Assume v is also volume preserving and that
x
'
(t) 0 for all x M and real t; then, if
x
t
: M M is weakly missng for some t, it is necessary that vx 0 at all x M. 相似文献
11.
Normality preserving multiplication operators 总被引:1,自引:0,他引:1
We show that a multiplication operator (T)=ATB is normality preserving if and only if it is hyponormality preserving, if and only if it is either of the formA=fg,B=h f, orA=D,B=D* for someC andD* D=I. Also we show that is (semi-) Fredholmness prserving if and only ifA andB are (semi-) Fredholm operators.Supported by the Science Foundation of Zhejiang Province and NSF. 相似文献
12.
Wolfgang Grotz 《Monatshefte für Mathematik》1979,88(3):219-228
LetK be an algebraic number field, and for every integer K let () andd(), respectively, denote the number of relatively prime residue classes and the number of divisors of the principal ideal (). Asymptotic equalities are proved for the sums () and d
2(), where runs through certain finite sets of integers ofK. 相似文献
13.
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
14.
We express the real connective K-theory groups
o4k–1(B
Q
) ofthe quaternion group Q
of order = 2
j
8 in terms of therepresentation theory of Q
by showing
o4k–1(B
Q
) =
Sp(S
4k+3/Q
)where is any fixed point free representation of Q
in U(2k + 2). 相似文献
15.
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
16.
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
17.
Mark Skandera 《Journal of Algebraic Combinatorics》2004,20(2):195-211
Let
I,I be the minor of a matrix which corresponds to row set I and column set I. We give a characterization of the inequalities of the form
I,I
K,K
J,J
L,L
which hold for all totally nonnegative matrices. This generalizes a recent result of Fallat, Gekhtman, and Johnson. 相似文献
18.
M. S. Sgibnev 《Mathematical Notes》1977,22(5):916-920
Let {n} be a sequence of identically distributed independent random variables,M1=<0,M
1
2
<;S
0=0,S
n
=1+2,+...+
n, n1;¯ S=sup {S
n
n=0.} The asymptotic behavior ofP(¯ St) as t is studied. If
t
P
(1x dx=0((t)), thenP(¯ St)– 1/¦¦
t
P (1x dx=0((t)) (t) is a positive function, having regular behavior at infinity.Translated from Matematicheskie Zametki, Vol. 22, No. 5, pp. 763–770, November, 1977.The author thanks B. A. Rogozin for the formulation of the problem and valuable remarks. 相似文献
19.
The long-known results of Schreier on group extensions are here raised to a categorical level by giving a factor set theory for torsors under a categorical group (G,) over a small category . We show a natural bijection between the set of equivalence classes of such torsors and [B({}),B(G,)], the set of homotopy classes of continuous maps between the corresponding classifying spaces. These results are applied to algebraically interpret the set of homotopy classes of maps from a CW-complex X to a path-connected CW-complex Y with
i
(Y)=0 for all i1,2. 相似文献
20.
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