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1.
We study pro-‘finite dimensional finite exponent’ completions of restricted Lie algebras over finite fields of characteristicp. These compact Hausdorff topological restricted Lie algebras, called pro-
restricted Lie algebras, are the restricted Lie-theoretic analogues of pro-p groups. A structure theory for pro-
restricted Lie algebras with finite rank is developed. In particular, the centre of such a Lie algebra is shown to be open.
As an application we examinep-adic analytic pro-p groups in terms of their associated pro-
restricted Lie algebras.
Supported by NSERC of Canada. 相似文献
2.
V. M. Petrogradsky 《Israel Journal of Mathematics》1999,113(1):323-339
Suppose that
% MathType!End!2!1! is a variety of Lie algebras, and letc
n(
% MathType!End!2!1!) be the dimension of the linear span of all multilinear words onn distinct letters in the free algebraF(
% MathType!End!2!1!,X) of the variety
% MathType!End!2!1!. We consider an exponential generating function
% MathType!End!2!1!, called the complexity function. The complexity function is an entire function of a complex variable provided
the variety of Lie algebras is nontrivial. In this paper we introduce the notion of complexity for Lie varieties in terms
of the growth of complexity functions; also we describe what the complexity means for the codimension growth of the variety.
Our main goal is to specify the complexity of a product of two Lie varieties in terms of the complexities of multiplicands.
The main observation here is thatC(
% MathType!End!2!1!),z) behaves like a composition of three functionsC(
% MathType!End!2!1!),z), exp(z), andC(
% MathType!End!2!1!),z).
Partially supported by grant RFFI 96-01-00146; the author is grateful to the University of Bielefeld for hospitality, where
he was DAAD-fellow. 相似文献
3.
Let G and H be Lie groups with Lie algebras
and
. Let G be connected. We prove that a Lie algebra homomorphism
is exact if and only if it is completely positive. The main resource is a corresponding theorem about representations on
Hilbert spaces.
This article summarizes the main results of [1].
Received: 6 December 2005 相似文献
4.
Özden Koruoğlu Recep Sahin Sebahattin İkikardes 《Bulletin of the Brazilian Mathematical Society》2007,38(1):51-65
We consider the extended Hecke groups
generated by T(z) = −1/z, S(z) = −1/(z + λ) and R(z) = 1/z with λ ≥ 2. In this paper, firstly, we study the fundamental region of the extended Hecke groups
. Then, we determine the abstract group structure of the commutator subgroups
, the even subgroup
, and the power subgroups
of the extended Hecke groups
. Also, finally, we give some relations between them. 相似文献
5.
Liviu I. Ignat Julio D. Rossi 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2008,59(5):918-925
In this paper we study the asymptotic behaviour as t → ∞ of solutions to a nonlocal diffusion problem on a lattice, namely, with t ≥ 0 and . We assume that J is nonnegative and verifies . We find that solutions decay to zero as t → ∞ and prove an optimal decay rate using, as our main tool, the discrete Fourier transform.
相似文献
6.
A family of transitive modular Lie superalgebras with depth one 总被引:1,自引:0,他引:1
Wen-de LIU~ 《中国科学A辑(英文版)》2007,50(10):1451-1466
The embedding theorem is established for Z-graded transitive modular Lie superalgebras g=(?)satisfying the conditions: (i)g0(?)(g-1)and g0-module g-1 is isomorphic to the natural(?)(g-1)-module; (ii)dim g1=2/3n(2n~2 1),where n=1/2dim g-1. In particular,it is proved that the finite-dimensional simple modular Lie superalgebras satisfying the conditions above are isomorphic to the odd Hamiltonian superalgebras.The restricted Lie superalgebras are also considered. 相似文献
7.
Benjamin Enriquez 《Selecta Mathematica, New Series》2007,13(3):391-463
We develop a cyclotomic analogue of the theory of associators. Using a trigonometric version of the universal KZ equations,
we prove the formality of a morphism , where B
n
1 is a braid group of type B. The formality isomorphism depends algebraically on a series ΨKZ, the “KZ pseudotwist”. We study the scheme of pseudotwists and show that it is a torsor under a group GTM(N, k), mapping to Drinfeld’s group GT(k), and whose Lie algebra is isomorphic to its associated graded (N, k). We prove that Ihara’s subgroup GTK of the Grothendieck–Teichmüller group, defined using distribution relations, in fact
coincides with it. We show that the subscheme of pseudotwists satisfying distribution relations is a subtorsor. We study the
corresponding analogue (N, k) of (N, k); it is a graded Lie algebra with an action of , and we give a lower bound for the character of its space of generators.
相似文献
8.
Hui-qiong Li Zhen-long Chenu 《应用数学学报(英文版)》2007,23(4):579-592
Let{(t);t∈R_ ~N}be a d-dimensional N-parameter generalized Brownian sheet.Necessaryand sufficient conditions for a compact set E×F to be a polar set for(t,(t))are proved.It is also provedthat if 2N≤αd,then for any compact set ER_>~N,d-2/2 Dim E≤inf{dimF:F ∈ B(R~d),P{(E)∩F≠φ}>0}≤d-2/β DimE,and if 2N>αd,then for any compact set FR~d\{0},α/2(d-DimF)≤inf{dimE:E∈B(R_>~N),P{(E)∩F≠φ}>0}≤β/2(d-DimF),where B(R~d)and B(R_>~N)denote the Borel σ-algebra in R~d and in R_>~N respectively,dim and Dim are Hausdorffdimension and Packing dimension respectively. 相似文献
9.
Milan Jasem 《Mathematica Slovaca》2007,57(2):107-118
In the paper isometries in pseudo MV-algebras are investigated. It is shown that for every isometry f in a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) there exists an internal direct decomposition
of
with
commutative such that
and
for each x ∈ A.
On the other hand, if
is an internal direct decomposition of a pseudo MV-algebra
= (A, ⊕, −, ∼, 0, 1) with
commutative, then the mapping g: A → A defined by
is an isometry in
and
.
相似文献
10.
The classical factorization method reduces the study of a system of ordinary differential equations Ut=[U+, U] to solving algebraic equations. Here U(t) belongs to a Lie algebra
which is the direct sum of its subalgebras
and
, where “+” signifies the projection on
. We generalize this method to the case
. The corresponding quadratic systems are reducible to a linear system with variable coefficients. It is shown that the generalized
version of the factorization method can also be applied to Liouville equation-type systems of partial differential equations.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 110, No. 3, pp. 339–350, March, 1997. 相似文献
11.
In this paper, we introduce Property ∏σ of operator algebras and prove that nest subalgebras and the finite-width CSL subalgebras of arbitrary von Neumann algebras have Property ∏σ.Finally, we show that the tensor product formula alg ML1-(×)algNL2 = algM-(×)N(L1 (×) L2) holds for any two finite-width CSLs L1 and L2 in arbitrary von Neumann algebras M and N, respectively. 相似文献
12.
Yu LI 《数学学报(英文版)》2008,24(2):285-304
Let G be a Lie group whose Lie algebra g is quadratic. In the paper "the non-commutative Weil algebra", Alekseev and Meinrenken constructed an explicit G-differential space homomorphism £, called the quantization map, between the Well algebra Wg = S(g^*) χ∧A(g^*) and Wg= U(g) χ Cl(g) (which they call the noncommutative Weil algebra) for g. They showed that £ induces an algebra isomorphism between the basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg). In this paper, we will interpret the quantization map .~ as the super Duflo map between the symmetric algebra S(Tg[1]) and the universal enveloping algebra U(Tg[1]) of a super Lie algebra T9[1] which is canonically associated with the quadratic Lie algebra g. The basic cohomology rings Hbas^*(Wg) and Hbas^*(Wg) correspond exactly to S(Tg[1])^inv and U(Tg[1])^inv, respectively. So what they proved is equivalent to the fact that the super Duflo map commutes with the adjoint action of the super Lie algebra, and that the super Duflo map is an algebra homomorphism when restricted to the space of invariants. 相似文献
13.
José M. Isidro 《Central European Journal of Mathematics》2007,5(3):512-522
Let G be the Banach-Lie group of all holomorphic automorphisms of the open unit ball
in a J*-algebra
of operators. Let
be the family of all collectively compact subsets W contained in
. We show that the subgroup F ⊂ G of all those g ∈ G that preserve the family
is a closed Lie subgroup of G and characterize its Banach-Lie algebra. We make a detailed study of F when
is a Cartan factor.
相似文献
14.
Chen Hua 《数学学报(英文版)》1997,13(1):81-89
In this paper, we study the asymptotic behaviour of the scattering phases(λ) of the Dirichlet Laplacian associated with obstacle
, where Ω is a bounded open subset of ℝ
n
(n≥2) with non-smooth boundary ∂Ω and connected complement Ω
e
=ℝ
n
. We can prove that if Ω satisfies a certain geometrical condition, then
where
,d
n>0 depending only onn, and |·|
j
(j = n - l, n) is aj- dimensional Lebesgue measure.
Research partially supported by the Natural Science Foundation of China and the Grant of Chinese State Education Committee 相似文献
15.
V. K. Kharchenko 《Algebra and Logic》1997,36(2):133-144
Let L be a finite-dimensional restricted differential Lie C-algebra of R-continuous derivations of a prime ring R of characteristic
p>0, with generalized centroid C. We prove that if the associative inner part of L is quasi-Frobenius then R contains a nonzero
element a and elements v1,…,vn, such that for any x∈R we have the expansion
, where
are homorphisms of right RL-modules
. This gives rise to a certain relation on a ring over some subring, known as Shirshov local finiteness. The structure of
(R, RL)-subbimodules in a left Martindale ring of quotients is elucidated.
Supported by RFFR grant No. 95-01-01356a, and by the CONACYT of Mexico, Catedra Patrimonial 940411.
Translated fromAlgebra i Logika, Vol. 36, No. 2, pp. 219–238, March–April, 1997. 相似文献
16.
Given a unital C*-algebra
and a right C*-module
over
, we consider the problem of finding short smooth curves in the sphere
= {x ∈
: 〈x, x〉 = 1}. Curves in
are measured considering the Finsler metric which consists of the norm of
at each tangent space of
. The initial value problem is solved, for the case when
is a von Neumann algebra and
is selfdual: for any element x
0 ∈
and any tangent vector ν at x
0, there exists a curve γ(t) = e
tZ
(x
0), Z ∈
, Z* = −Z and ∥Z∥ ≤ π, such that γ(0) = x
0 and
(0) = ν, which is minimizing along its path for t ∈ [0, 1]. The existence of such Z is linked to the extension problem of selfadjoint operators. Such minimal curves need not be unique. Also we consider the
boundary value problem: given x
0, x
1 ∈
, find a curve of minimal length which joins them. We give several partial answers to this question. For instance, let us
denote by f
0 the selfadjoint projection I − x
0 ⊗ x
0, if the algebra f
0
f
0 is finite dimensional, then there exists a curve γ joining x
0 and x
1, which is minimizing along its path.
相似文献
17.
Zhu Yaochen 《数学学报(英文版)》1988,4(4):364-371
Let
be a finitely generated extension field of ℚ, andα
i,βj(1⩽i⩽m,1⩽j⩽n) be some complex numbers. Let
(k=1,2,3) be fields obtained by adjoining to
the numbers {α
i,βj exp(αiβj)}, {αi, exp(αiβj)}, and {exp(αiβj)}, respectively. In the present note the relation between the transcendental degree of
over
and the transcendence type of
over ℚ is given.
This work was completed in Dpt. Math., Univ. of Southern Mississippi, Hattiesburg, USA. 相似文献
18.
19.
We prove that for almost allσ ∈G ℚ the field
has the following property: For each absolutely irreducible affine varietyV of dimensionr and each dominating separable rational mapϕ:V→
there exists a point a ∈
such thatϕ(a) ∈ ℤr. We then say that
is PAC over ℤ. This is a stronger property then being PAC. Indeed we show that beside the fields
other fields which are algebraic over ℤ and are known in the literature to be PAC are not PAC over ℤ. 相似文献
20.
S. G. Dani 《manuscripta mathematica》1992,74(1):445-452
We prove that ifG is a connected Lie group with no compact central subgroup of positive dimension then the automorphism group ofG is an almost algebraic subgroup of
, where
is the Lie algebra ofG. We also give another proof of a theorem of D. Wigner, on the connected component of the identity in the automorphism group
of a general connected Lie group being almost algebraic, and strengthen a result of M.Goto on the subgroup consisting of all
automorphisms fixing a given central element. 相似文献