共查询到20条相似文献,搜索用时 31 毫秒
1.
V. Yu. Popov 《Algebra and Logic》2001,40(1):55-66
It is proved that there exists an infinite sequence of finitely based semigroup varieties
such that, for all i, an equational theory for
and for the class
of all finite semigroups in
is undecidable while an equational theory for
and for the class
of all finite semigroups in
is decidable. An infinite sequence of finitely based semigroup varieties
is constructed so that, for all i, an equational theory for
and for the class
of all finite semigroups in
is decidable whicle an equational theory for
and for the class
of all finite semigroups in
is not. 相似文献
2.
David A. Richter 《Acta Appl Math》2001,66(1):41-65
Starting from the commutation relations in a complex semisimple Lie algebra
, one may obtain a space
of vector fields on Euclidean space such that
and
are isomorphic when
is equipped with the usual Lie bracket between vector fields and the isotropy subalgebra of
is a Borel subalgebra
. Furthermore, one may adjoin to the vector fields in
multiplication operators to obtain an
-parameter family of distinct presentations of
as spaces of differential operators, where
is the dual of a Cartan subalgebra. Some of these presentations will preserve a space of polynomials on Euclidean space, and, in fact, all the finite-dimensional representations of
can be presented in this way. All of this is carried out explicitly for arbitrary
. In doing so, one discovers there is a Lie group of diffeomorphisms of the unipotent subgroup N complementary to B which acts on these presentations and preserves a certain notion of weight. 相似文献
3.
D. I. Panyushev 《Functional Analysis and Its Applications》2004,38(1):38-44
Let
be a reductive Lie algebra over an algebraically closed field of characteristic zero and
an arbitrary
-grading. We consider the variety
, which is called the commuting variety associated with the
-grading. Earlier it was proved by the author that
is irreducible, if the
-grading is of maximal rank. Now we show that
is irreducible for
and (E6,F4). In the case of symmetric pairs of rank one, we show that the number of irreducible components of
is equal to that of nonzero non--regular nilpotent G
0-orbits in
. We also discuss a general problem of the irreducibility of commuting varieties. 相似文献
4.
V. V. Kornienko 《Mathematical Notes》2000,68(5-6):576-587
We study the distribution in the complex plane
of the spectrum of the operator
, generated by the closure in
of the operation
originally defined on smooth functions
with values in a Hilbert space
satisfying the Dirichlet conditions
. Here
and A is a model operator acting in
. Criterial conditions on the parameter
for the eigenfunctions of the operator
to form a complete and minimal system as well as a Riesz basis in the Hilbert space H are given. 相似文献
5.
On a Problem of the Theory of Multiply Local Formations 总被引:1,自引:0,他引:1
We describe the -closed n-multiply local formations
such that the lattice of all -closed n-multiply local formations between
and
is Boolean. 相似文献
6.
Any transversally holomorphic foliated map
of Kählerianfoliations with
harmonic, is shown to be a transversallyharmonic map and an absolute minimum of the energy functional
inits foliated homotopy class. 相似文献
7.
For an arbitrary variety
of groups and an arbitrary class
of groups that is closed on quotient groups, we prove that a quotient group G/N of the group G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) if G possesses an invariant system with
- and
-factors (respectively, is a residually
-group) and N
(respectively, N is a maximal invariant
-subgroup of the group G). 相似文献
8.
A nondegenerate null-pair of the real projective space
consists of a point and of a hyperplane nonincident to this point. The manifold of all nondegenerate null-pairs
carries a natural Kählerian structure of hyperbolic type and of constant nonzero holomorphic sectional curvature. In particular,
is a symplectic manifold. We prove that
is endowed with the structure of a fiber bundle over the projective space
, whose typical fiber is an affine space. The vector space associated to a fiber of the bundle is naturally isomorphic to the cotangent space to
. We also construct a global section of this bundle; this allows us to construct a diffeomorphism
between the manifold of nondegenerate null-pairs and the cotangent bundle over the projective space. The main statement of the paper asserts that the explicit diffeomorphism
is a symplectomorphism of the natural symplectic structure on
to the canonical symplectic structure on
. 相似文献
9.
We construct the trajectory attractor
of a three-dimensional Navier--Stokes system with exciting force
. The set
consists of a class of solutions to this system which are bounded in
, defined on the positive semi-infinite interval
of the time axis, and can be extended to the entire time axis
so that they still remain bounded-in-
solutions of the Navier--Stokes system. In this case any family of bounded-in-
solutions of this system comes arbitrary close to the trajectory attractor
. We prove that the solutions
are continuous in t if they are treated in the space of functions ranging in
. The restriction of the trajectory attractor
to
,
, is called the global attractor of the Navier--Stokes system. We prove that the global attractor
thus defined possesses properties typical of well-known global attractors of evolution equations. We also prove that as
the trajectory attractors
and the global attractors
of the
-order Galerkin approximations of the Navier--Stokes system converge to the trajectory and global attractors
and
, respectively. Similar problems are studied for the cases of an exciting force of the form
depending on time
and of an external force
rapidly oscillating with respect to the spatial variables or with respect to time
. 相似文献
10.
V. Yu. Popov 《Algebra and Logic》2005,44(1):46-54
There exist independently based semigroup varieties
and
,
, such that
has no cover in the interval [
;
].Translated from Algebra i Logika, Vol. 44, No. 1, pp. 81–96, January–February, 2005. 相似文献
11.
M. B. Zvyagina 《Journal of Mathematical Sciences》2004,120(4):1591-1602
Let
be an associative ring with identity, and let
be the category of left unitary
-modules. A complete characterization of continuous additive co- and contravariant functors
is given. Such functors are either representable, or equivalent to a tensor product, or trivial ones. The class of categories that are dual to
and, therefore, are equivalent to the category of compact right
-modules is constructed by purely algebraic means. A canonical category is singled out in this class. A purely algebraic structure that is equivalent to the topology-algebraic structure of compact right
-modules is constructed. Algebraic analogs of connection and complete disconnection are given. Bibliography: 6 titles. 相似文献
12.
We introduce the notion of hyper-self-duality for Bose-Mesner algebras as a strengthening of formal self-duality. Let
denote a Bose-Mesner algebra on a finite nonempty set X. Fix p X, and let
and
denote respectively the dual Bose-Mesner algebra and the Terwilliger algebra of
with respect to p. By a hyper-duality of
, we mean an automorphism of
such that
for all
; and
is a duality of
.
is said to be hyper-self-dual whenever there exists a hyper-duality of
. We say that
is strongly hyper-self-dual whenever there exists a hyper-duality of
which can be expressed as conjugation by an invertible element of
. We show that Bose-Mesner algebras which support a spin model are strongly hyper-self-dual, and we characterize strong hyper-self-duality via the module structure of the associated Terwilliger algebra. 相似文献
13.
14.
In this paper we define a lattice order on a set F of binary functions. We then provide necessary and sufficient conditions for the resulting algebra
F to be a distributive lattice or a Boolean algebra. We also prove a Cayley theorem for distributive lattices by showing that for every distributive lattice
, there is an algebra
F of binary functions, such that
is isomorphic to
F and we show that
F is a distributive lattice iff the operations and are idempotent and cummutative, showing that this result cannot be generalized to non-distributive lattices or quasilattices without changing the definitions of and . We also examine the equational properties of an Algebra
for which
, now defined on the set of binary
-polynomials is a lattice or Boolean algebra. 相似文献
15.
Ignacio Bajo 《Monatshefte für Mathematik》1994,118(1-2):1-6
Let
be a complex Lie algebra,
its underlying real Lie algebra,
a real form of
and ·, · the euclidean product induced by the real part of an hermitian inner product on
. Let aut
be the Lie algebra of skew-symmetric derivations of
. We give necessary and sufficient conditions to ensure that aut
is composed of skew-hermitian derivations. As an application, we study holomorphy in large subgroups of isometries of Lie groups. 相似文献
16.
Avishay Vaknin 《K-Theory》2001,24(1):57-68
For a small triangulated category
, Bass's K
1 group
is described, and the theorem of the heart is proved. We define the determinant map from
to Neeman's
, and we compute this map when
is the derived category of an Abelian category
. 相似文献
17.
Let
be an entire function of finite type with respect to finite order
and let
be a subset of an open cone in a certain n-dimensional subspace
(the smaller
, the sparser
). We assume that this cone contains a ray
0} \right\}$$
" align="middle" border="0">
. It is shown that the radial indicator
of
at any point
may be evaluated in terms of function values at points of the discrete subset
. Moreover, if
tends to zero fast enough as
over
, then this function vanishes identically. To prove these results, a special approximation technique is developed. In the last part of the paper, it is proved that, under certain conditions on
and
, which are close to exact conditions, the function
bounded on
is bounded on the ray. 相似文献
18.
Two numerical characteristics of a nonrectifiable arc
generalizing the notion of length are introduced. Geometrically, this notion can naturally be generalized as the least upper bound of the sums
, where
are the lengths of segments of a polygonal line inscribed in the curve
and
is a given function. On the other hand, the length of
is the norm of the functional
in the space
; its norms in other spaces can be considered as analytical generalizations of length. In this paper, we establish conditions under which the generalized geometric rectifiability of a curve
implies its generalized analytic rectifiability. 相似文献
19.
We prove the absolute continuity of the spectrum of the Schrödinger operator in
,
, with periodic (with a common period lattice
) scalar
and vector
potentials for which either
,
, or the Fourier series of the vector potential
converges absolutely,
, where
is an elementary cell of the lattice
,
for
, and
for
, and the value of
is sufficiently small, where
and
otherwise,
, and
. 相似文献
20.
D. M. Smirnov 《Algebra and Logic》2003,42(2):136-146
We continue to study interrelations between permutative varieties and the cyclic varieties defined by cycles of the form
. A criterion is given determining whether a cyclic variety
is interpretable in
. For a permutation
without fixed elements, it is stated that a set of primes
for which
is interpretable in
in the lattice
is finite. It is also proved that for distinct primes
, the Helly number of a type
in
coincides with dimension of the dual type
and equals
. 相似文献