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1.
Let be a field of characteristic zero and let be a two- dimensional non-associative algebra over . We prove that the sequence of codimensions of is either bounded by or grows exponentially as . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is , . 相似文献
2.
Let be a function algebra on a locally compact Hausdorff space. A linear isometry is said to be of codimension if the range of has codimension in . In this paper, we provide and study a classification of codimension 1 linear isometries on function algebras in general and on Douglas algebras in particular. 相似文献
3.
Here we define decomposable pseudometrics. A pseudometric is decomposable if it can be represented as the sum of two pseudometrics
that are obtained in a way other than the multiplication all distances by a positive factor. We consider spaces consisting
of n points. We prove that there exist a finite number of indecomposable pseudometrics (that is, a basis) such that any pseudometric
is a linear combination of basic pseudometrics with nonnegative coefficients. For n ≤ 7, the basic pseudometrics are listed. A decomposability test is derived for finite pseudometric spaces. We also establish
some other conditions of decomposability and indecomposability.
Translated from Matematicheskie Zametki, Vol. 63, No. 2, pp. 225–234, February, 1998. 相似文献
5.
Let f, g : X→Y be two maps between closed manifolds with dim X ≥ dim Y = n ≥ 3. We study the primary obstruction on(f, g) to deforming f and g to be coincidence free on the n-th skeleton of X. We give examples for which obstructions to deforming f and g to be coincidence free are detected by on (f, g). 相似文献
6.
We give an example showing that the Kobayashi–Royden pseudometric for a pseudoconvex domain is, in general, not the derivative of the Lempert function. 相似文献
7.
A celebrated theorem of Kemer (1978) states that any algebra satisfying a polynomial identity over a field of characteristic zero is PI-equivalent to the Grassmann envelope of a finite dimensional superalgebra . In this paper, by exploiting the basic properties of the exponent of a PI-algebra proved by Giambruno and Zaicev (1999), we define and classify the minimal superalgebras of a given exponent over a field of characteristic zero. In particular we prove that these algebras can be realized as block-triangular matrix algebras over the base field. The importance of such algebras is readily proved: is a minimal superalgebra if and only if the ideal of identities of is a product of verbally prime T-ideals. Also, such superalgebras allow us to classify all minimal varieties of a given exponent i.e., varieties such that and for all proper subvarieties of . This proves in the positive a conjecture of Drensky (1988). As a corollary we obtain that there is only a finite number of minimal varieties for any given exponent. A classification of minimal varieties of finite basic rank was proved by the authors (2003). As an application we give an effective way for computing the exponent of a T-ideal given by generators and we discuss the problem of what functions can appear as growth functions of varieties of algebras. 相似文献
11.
The splitting obstruction groups depend functorially on the square of fundamental groups. In the paper the problem of splitting along a submanifold of codimension two under some restrictions on the square of fundamental groups is considered. New exact sequences and commutative diagrams containing Wall groups, splitting obstruction groups, and surgery obstruction groups for manifold pairs are obtained. Examples of computation of splitting obstruction groups and natural maps are considered. 相似文献
12.
We study codimension 2 homogeneous submanifolds of Euclidean space for which the index of minimum relative nullity is small. We prove that if min xMf(x)n-5, where (x) denotes the nullity of the second fundamental form of the immersion f at the point x, then the manifold M
n
is either isometric to a sphere or to a product of two spheres S 2×S
n–2
or covered by the Riemannian product S
n–1
×R. As a consequence, we obtain a classification of compact codimension 2 homogeneous submanifolds of dimension at least 5. 相似文献
13.
We continue the study of indecomposable finite (consisting of a finite number of points) pseudometric spaces (i.e., spaces
whose only decomposition into a sum is the division of all distances in equal proportion). We prove that the indecomposability
property is invariant under the following operation: connect two disjoint points by an additional simple chain, which is the
inverted copy of the shortest path connecting these points. The indecomposability of the spaces presented by the graphs K
m,n
( m ≥ 2, n ≥ 3) with edges of equal length is also proved.
Translated from Matematicheskie Zametki, Vol. 63, No. 3, pp. 421–424, March, 1998. 相似文献
15.
A calculation formula is established for the codimension of the polynomial subspace in with discrete indeterminate measure . We clarify how much the masspoint of the -canonical solution of an indeterminate Hamburger moment problem differs from the masspoint of the corresponding -extremal solution at a given point of the real axis. 相似文献
16.
In this paper some non existence results are given for smooth varieties of dimension bigger then 1, embedded in projective spaces with low codimension, by the pluricanonical system | mK X |, with m≥2. The only meaningful cases of codimension 2 are surfaces in P 4 and threefolds in P 5, whose existence is excluded. When the codimension is 3, for surfaces in P 5 is proven that m=2, while for three-folds in P 6 and fourfolds in P 7 only two numerical possibilities for the degree are given. 相似文献
18.
We single out the obstruction for a closed
-null-homologous submanifold of codimension 2 to be the boundary of a submanifold of codimension 1. As an application, we calculate the groups
of cobordisms of embeddings of nonoriented n-manifolds in the Euclidean ( n+2)-space for n=3 and 4. Namely, we show that
and
. A specific generator of the former group is explicitly given. Bibliography: 5 titles. 相似文献
19.
In this short note we give a complete characterization of a certain class of compact corank one Poisson manifolds, those equipped with a closed one-form defining the symplectic foliation and a closed two-form extending the symplectic form on each leaf. If such a manifold has a compact leaf, then all the leaves are compact, and furthermore the manifold is a mapping torus of a compact leaf. These manifolds and their regular Poisson structures admit an extension as the critical hypersurface of a b-Poisson manifold as we will see in [9]. 相似文献
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