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1.
A. I. Budkin 《Algebra and Logic》2007,46(1):16-27
We fix a universal algebra A and its subalgebra H. The dominion of H in A (in a class M) is the set of all elements a ∈ A such that any pair of homomorphisms f, g: A → M ∈ M satisfies the following: if f and g coincide on H then f(a) = g(a). In association with every quasivariety, therefore, is
a dominion of H in A. Sufficient conditions are specified under which a set of dominions form a lattice. The lattice of dominions
is explored for down-semidistributivity. We point out a class of algebras (including groups, rings) such that every quasivariety
in this class contains an algebra whose lattice of dominions is anti-isomorphic to a lattice of subquasivarieties of that
quasivariety.
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Translated from Algebra i Logika, Vol. 46, No. 1, pp. 26–45, January–February, 2007. 相似文献
2.
Let V be a variety of algebras. We specify a condition (the so-called generalized entropic property), which is equivalent to the
fact that for every algebra A ∈ V, the set of all subalgebras of A is a subuniverse of the complex algebra of the subalgebras of A. The relationship between the generalized entropic property and the entropic law is investigated. Also, for varieties with
the generalized entropic property, we consider identities that are satisfied by complex algebras of subalgebras.
Dedicated to George Gr?tzer on the occasion of his 70th birthday
Supported by INTAS grant No. 03-51-4110.
Supported by MŠMTČR (project MSM 0021620839) and by the Grant Agency of the Czech Republic (grant No. 201/05/0002).
Translated from Algebra i Logika, Vol. 47, No. 6, pp. 655–686, November–December, 2008. 相似文献
3.
We compute the largest dimension of the Abelian Lie subalgebras contained in the Lie algebra
of n×n strictly upper triangular matrices, where n ∈ ℕ \ {1}. We do this by proving a conjecture, which we previously advanced,
about this dimension. We introduce an algorithm and use it first to study the two simplest particular cases and then to study
the general case.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 419–429, September, 2007. 相似文献
4.
O. V. Markova 《Journal of Mathematical Sciences》2008,155(6):908-931
Let {ie910-01} be a field and let {ie910-02} be a finite-dimensional {ie910-03}-algebra. We define the length of a finite
generating set of this algebra as the smallest number k such that words of length not greater than k generate {ie910-04} as a vector space, and the length of the algebra is the maximum of the lengths of its generating sets.
In this article, we give a series of examples of length computation for matrix subalgebras. In particular, we evaluate the
lengths of certain upper triangular matrix subalgebras and their direct sums, and the lengths of classical commutative matrix
subalgebras. The connection between the length of an algebra and the lengths of its subalgebras is also studied.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 13, No. 4, pp. 165–197, 2007. 相似文献
5.
We investigate two systematic constructions of inverse-closed subalgebras of a given Banach algebra or operator algebra $\ensuremath {\mathcal {A}}We investigate two systematic constructions of inverse-closed subalgebras of a given Banach algebra or operator algebra A\ensuremath {\mathcal {A}}, both of which are inspired by classical principles of approximation theory. The first construction requires a closed derivation
or a commutative automorphism group on A\ensuremath {\mathcal {A}} and yields a family of smooth inverse-closed subalgebras of A\ensuremath {\mathcal {A}} that resemble the usual H?lder–Zygmund spaces. The second construction starts with a graded sequence of subspaces of A\ensuremath{\mathcal{A}} and yields a class of inverse-closed subalgebras that resemble the classical approximation spaces. We prove a theorem of
Jackson–Bernstein type to show that in certain cases both constructions are equivalent. 相似文献
6.
A. I. Budkin 《Siberian Mathematical Journal》2010,51(3):396-401
The dominion of a subgroup H of a group A in a quasivariety ℳ is the set of all a ∈ A with equal images under all pairs of homomorphisms from A into every group in ℳ which coincide on H. The concept of dominion provides some closure operator on the lattice of subgroups of a given group. We study the closed
subgroups with respect to this operator. We find a condition for the dominion of a divisible subgroup in quasivarieties of
metabelian groups to coincide with the subgroup. 相似文献
7.
王晓明 《数学年刊A辑(中文版)》2016,37(4):397-404
设g=W_1是特征p3的代数闭域k上的Witt代数.本文确定了g的极大基本子代数.进一步具体给出了最大维数的基本子代数的G共轭类,这里G是g的自同构群.从而证明了最大维数为(p-1)/2的基本子代数射影簇E((p-1)/2,g)是不可约的且是一维的.更进一步,证明了E(1,g)是不可约的,具有维数p-2,而E(2,g)是等维的,共有(p-3)/2个不可约分支,且每个不可约分支的维数是p-4.而当3≤r≤(p-3)/2时,E(r,g)是可约的.给出了E(r,g)(3≤r≤(p-3)/2)维数的一个下界. 相似文献
8.
If
\mathfrakA{\mathfrak{A}} is a unital weak-* closed algebra of multiplication operators on a reproducing kernel Hilbert space which has the property
\mathbbA1(1){\mathbb{A}_1(1)}, then the cyclic invariant subspaces index a Nevanlinna–Pick family of kernels. This yields an NP interpolation theorem for
a wide class of algebras. In particular, it applies to many function spaces over the unit disk including Bergman space. We
also show that the multiplier algebra of a complete NP space has
\mathbbA1(1){\mathbb{A}_1(1)}, and thus this result applies to all of its subalgebras. A matrix version of this result is also established. It applies,
in particular, to all unital weak-* closed subalgebras of H
∞ acting on Hardy space or on Bergman space. 相似文献
9.
CaiShiWANG ZhiYuanHUANG 《数学学报(英文版)》2004,20(6):999-1008
A family of closed snbalgebras, indexed by R(the set of real numbers), of the Wick algebra is constructed. Fundamental properties of tile family are shown including the increasing property and the right-continuity. The notion of adaptedness to the family is defined for quantum stochastic processes in terms of generalized operators. The existence and uniqueness of solutions adapted to the family is established for quantum stochastic differential equations in terms of generalized operators. 相似文献
10.
A. A. Zorin 《Functional Analysis and Its Applications》2009,43(2):119-131
Let G be a reductive algebraic group over an algebraically closed field of characteristic zero, and let \(\mathfrak{h}\) be an algebraic subalgebra of the tangent Lie algebra \(\mathfrak{g}\) of G. We find all subalgebras \(\mathfrak{h}\) that have no nontrivial characters and whose centralizers \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} \) and \(P(\mathfrak{g})^\mathfrak{h} \) in the universal enveloping algebra \(\mathfrak{U}(\mathfrak{g})\) and in the associated graded algebra \(P(\mathfrak{g})\), respectively, are commutative. For all these subalgebras, we prove that \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} = \mathfrak{U}(\mathfrak{h})^\mathfrak{h} \otimes \mathfrak{U}(\mathfrak{g})^\mathfrak{g} \) and \(P(\mathfrak{g})^\mathfrak{h} = P(\mathfrak{h})^\mathfrak{h} \otimes P(\mathfrak{g})^\mathfrak{g} \). Furthermore, we obtain a criterion for the commutativity of \(\mathfrak{U}(\mathfrak{g})^\mathfrak{h} \) in terms of representation theory. 相似文献
11.
D. A. Anikeeva 《Journal of Mathematical Sciences》2008,152(6):817-825
Let ξ(t), t ∈ [0, 1], be a tempered stable process. By {ie4447-01} we denote the law of ξ in the Skorokhod space {ie4447-02}.
For the measure {ie4447-03}, we construct the group of nonsingular transformations of {ie4447-04}. Bibliography: 10 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 38–53. 相似文献
12.
N. V. Smorodina 《Journal of Mathematical Sciences》2008,152(6):934-940
Let ξ(t), t ∈ [0, 1], be an α-stable Lévy process in ℝd. Denote by {ie4563-01} the measure generated by ξ in the Skorokhod space {ie4563-02}. Under some conditions on the spectral
measure of the process ξ, we construct a group of {ie4563-03}-preserving transformations of {ie4563-04}. Bibliography: 12
titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 351, 2007, pp. 242–252. 相似文献
13.
In recent years much work has been done analyzing maps, not assumed to be linear, between uniform algebras that preserve the
norm, spectrum, or subsets of the spectra of algebra elements, and it is shown that such maps must be linear and/or multiplicative.
Letting A and B be uniform algebras on compact Hausdorff spaces X and Y, respectively, it is shown here that if λ ∈ ℂ / {0} and T: A → B is a surjective map, not assumed to be linear, satisfying
then T is an ℝ-linear isometry and there exist an idempotent e ∈ B, a function κ ∈ B with κ
2 = 1, and an isometric algebra isomorphism such that
for all f ∈ A, where γ = λ / |λ|. Moreover, if T is unital, i.e. T(1) = 1, then T(i) = i implies that T is an isometric algebra isomorphism whereas T(i) = −i implies that T is a conjugate-isomorphism.
相似文献
14.
We give a precise expression for the universal weight function of the quantum affine algebra U
q
(
). The calculations use the technique of projecting products of Drinfeld currents on the intersections of Borel subalgebras.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 1, pp. 3–34, October, 2005. 相似文献
15.
16.
Weak Hopf Algebras Corresponding to Borcherds-Cartan Matrices 总被引:1,自引:0,他引:1
Li Xia YE Zhi Xiang WU Xue Feng MEI 《数学学报(英文版)》2007,23(10):1729-1744
Let y be a generalized Kac-Moody algebra with an integral Borcherds-Cartan matrix. In this paper, we define a d-type weak quantum generalized Kac-Moody algebra wUq^d(y), which is a weak Hopf algebra. We also study the highest weight module over the weak quantum algebra wUdq^d(y) and weak A-forms of wUq^d(y). 相似文献
17.
We investigate regular hyperbolic subalgebras of hyperbolic Kac–Moody algebras via their Weyl groups. We classify all subgroup
relations between Weyl groups of hyperbolic Kac–Moody algebras, and show that for every pair of a group and subgroup there
exists at least one corresponding pair of algebra and subalgebra. We find all types of regular hyperbolic subalgebras for
a given hyperbolic Kac–Moody algebra, and present a finite algorithm classifying all embeddings. 相似文献
18.
W.M. Priestly 《Semigroup Forum》1998,56(3):301-322
t , for t ≥ 0, be a strongly continuous Markovian semigroup acting on C(X), where X is a compact Hausdorf space, and let D
denote the domain of its infinitesimal generator Z. Suppose D contains a (perhaps finite) family of functions f separating
the points of X and satisfying Zf2 = 2fZf. If either
(1) there exists δ > 0 such that (Tt f)2∈ D if 0 ≤ t ≤δ for each f in this family; or
(1′) for some core D′ of Z, g ∈ D′ implies g2∈ D, then the underlying Markoff process on X is deterministic. That is, there exists a semiflow — a semigroup (under composition)
of continuous functions φt from X into X — such that Ttf(x) = f(φt (x)). If the domain D should be an algebra then conditions (1) and (1′) hold trivially. Conversely, if we have a separating
family satisfying Zf2 = 2fZf then each of these conditions implies that D is an algebra. It is an open question as to whether these conditions
are redundant. If the functions φt are homeomorphisms from X onto X, then of course we have a Markovian group induced by a flow. This result is obtained by
first providing general results about the null-space N of the (function-valued) positive semidefinite quadratic form defined
by < f, g > = Z(fg) - fZg - gZf. The set N can be defined for any generator Z of a strongly continuous Markovian semigroup
and is equivalently given by
N = {f ∈ D| f2∈ D and Zf2 = 2fZf}
= {f ∈ D| Tt(f2)-(Ttf)2 is o(t2) in C(X)}.
In the general case N is an algebra closed under composition with any C1-function φ from the reals to the reals, and Z(φ[f]) = (Zf)φ′[f] if f ∈ N. This "chain rule" on N (on which Z must act as
a derivation) is a special case of a theorem for C2-functions φ which holds more generally for all f in d, viz.,
Z(φ[f] = (Zf) φ′[f] + ? <f, f> φ″[f],
Provided Z is a local operator and D is an algebra. In this case the form < f, g > itself enjoys the relation
< φ[f], ψ[g] > = φ′ [f] ψ′[g] < f, g >,
for C2functions φ and ψ. Some of the results and their proofs continue to hold when the setting is switched from the commutative
C*-algebra C(X) to a general (noncommutative) C*-algebra A. In the norm continuous case we obtain a sharp characterization
of Markovian semigroups that are groups: Let Tt = etz , defined for t ≥ 0, be a Markovian semigroup acting on a C*-algebra A that is norm continuous, i.e., ||Tt - I|| ⇒ 0 as t ⇒ 0 +. Assume Z(a2) = a(Za) + (Za) a for some (perhaps finite) set of self-adjoint elements a that generate a Jordan algebra dense among the
self-adjoint elements of A. The etz , -∞ < t < ∞, is a group of Markovian operators. 相似文献
19.
Free Akivis algebras and primitive elements in their universal enveloping algebras are investigated. It is proved that subalgebras of free Akivis algebras are free and that finitely generated subalgebras are finitely residual. Decidability of the word problem for the variety of Akivis algebras is also proved.The conjecture of K. H. Hofmann and K. Strambach (Problem 6.15 in [Topological and analytic loops, in “Quasigroups and Loops Theory and Applications,” Series in Pure Mathematics (O. Chein, H. O. Pflugfelder, and J. D. H. Smith, Eds.), Vol. 8, pp. 205–262, Heldermann Verlag, Berlin, 1990]) on the structure of primitive elements is proved to be not valid, and a full system of primitive elements in free nonassociative algebra is constructed.Finally, it is proved that every algebra B can be considered as a hyperalgebra, that is, a system with a series of multilinear operations that plays a role of a tangent algebra for a local analytic loop, where the hyperalgebra operations on B are interpreted by certain primitive elements. 相似文献
20.
The Maximal Graded Left Quotient Algebra of a Graded Algebra1) 总被引:1,自引:0,他引:1
Gonzalo ARANDA PINO Mercedes SILES MOLINA 《数学学报(英文版)》2006,22(1):261-270
We construct the maximal graded left quotient algebra of every graded algebra A without homogeneous total right zero divisors as the direct limit of graded homomorphisms (of left A-modules) from graded dense left ideals of A into a graded left quotient algebra of A. In the case of a superalgebra, and with some extra hypothesis, we prove that the component in the neutral element of the group of the maximal graded left quotient algebra coincides with the maximal left quotient algebra of the component in the neutral element of the group of the superalgebra. 相似文献