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1.
Michel Duflo 《Inventiones Mathematicae》1982,67(3):385-393
Résumé Soient
une algèbre de Lie de dimension finie et
une sousalgèbre de Lie de
. Je montre que l'induction, qui envoie les idéaux de l'algèbre enveloppante de
dans les idéaux de l'algèbre enveloppante de
, commute, à une torsion près, à l'anti-automorphisme principal. La résolution libre standard de la représentation triviale d'une algèbre de Lie joue un rôle important dans la démonstration.
Convention. On fixe un corps commutatifk. Tous les espaces vectoriels, produits tensoriels et algèbres considérés dans cet article sont surk.
Notations. Si g est une algèbre de Lie, on noteU(g) son algèbre enveloppante. On noteu l'anti-automorphisme principal deU(g): c'est l'antiautomorphisme tel que pourXg. Si est une forme linéaire sur g, nulle sur [g,g], on noteuu
l'automorphisme deU(g) tel queX
=X+(X) pourXg. Si g est de dimension finie, la fonction module de g est la forme linéaireXtradX. 相似文献
Summary Let be a finite dimensional Lie algebra, and a Lie subalgebra. I show that the induction map, between the sets of ideals in the enveloping algebras of and , commutes, up to a twisting, with the principal anti-automorphism. The standard free resolution of the trivial representation of a Lie algebra plays an important role in the proof.
Convention. On fixe un corps commutatifk. Tous les espaces vectoriels, produits tensoriels et algèbres considérés dans cet article sont surk.
Notations. Si g est une algèbre de Lie, on noteU(g) son algèbre enveloppante. On noteu l'anti-automorphisme principal deU(g): c'est l'antiautomorphisme tel que
2.
V. Ostrik 《Transformation Groups》1997,2(3):279-287
We study the tensor category
of tilting modules over a quantum groupU
q
with divided powers. The setX
+ of dominant weights is a union of closed alcoves
numbered by the elementswW
f
of a certain subset of affine Weyl groupW. G. Lusztig and N. Xi defined a partition ofW
f
into canonical right cells and the right order
R
on the set of cells. For a cellAW
f
we consider a full subcategory
formed by direct sums of tilting modulesQ() with highest weights
. We prove that
is a tensor ideal in
, generalizing H. Andersen's theorem about the ideal of negligible modules which in our notations is nothing else then
. The proof is an application of a recent result by W. Soergel who has computed the characters of tilting modules.This material is based upon work supported by the U.S. Civilian Research and Development Foundation under Award No. RM1-265. 相似文献
3.
Let
and
the foliations by the null geodesics of some lorentzian metricg on the torus
. We analyse how geodesic completeness properties ofg are related to the dynamics of
and
. 相似文献
4.
Let
be a semisimple Lie algebra overk, an algebraically closed field of characteristic zero, and let
be a Cartan subalgebra inside a Borel subalgebra of
. LetU be the enveloping algebra of
. For
letM() denote the corresponding Verma modúle and letU
u=U/AnnM(). LetW be the Weyl group and letW
0
be the stabiliser of inW. We prove the following theorem, which affirms a conjecture of T.J. Hodges.Oblatum 16-XII-1994 相似文献
5.
Ton Daorong 《数学学报(英文版)》1990,6(1):47-56
In this paper we discuss the completions (,
) of a commutativel-groupG with respect to the intrinsic topologies . We give some conditions under which
is the intrinsic topology of the same type on as
and give the relations between these completions. 相似文献
6.
By combinatorial means the authors show the existence of thin sub-sets of primes, useful for Goldbach decompositions. For example, there is a set
of primes with
, such that all butO(x(ln x)–A) even integersnx can be written as
. 相似文献
7.
Ralph McKenzie 《Algebra Universalis》1984,18(1):29-69
A construction is defined which associates, to every algebra
of a fixed but arbitrary finite similarity type, a groupoidF
. The identities ofF
are finitely based if and only if those of
are, andF
is finite if and only if
is finite. Up to isomorphism,F
has the same endomorphism monoid and subalgebra lattice as
, but the congruence lattice ofF
is the result of adjoining a new 1 to the congruence lattice of
.F is functorial, preserves the satisfaction (and the non-satisfaction) of most Mal'cev conditions, and produces, by composition with the operation of forming the generated variety, an isomorphism of the lattice of varieties of fixed type to an interval in the lattice of varieties of groupoids.The construction makes use of a new product operation, applicable to two algebras of differing similarity types, which is introduced and studied in this paper.Research supported by National Science Foundation grant MCS-8103455.Presented by K. A. Baker. 相似文献
8.
M. Emery 《Probability Theory and Related Fields》1980,51(1):95-100
Summary Let (,
, P) be a complete probability space; let
t0 be an increasing right-continuous family of
-complete sub--fields of
; let
be a sequence of semimartingales. Assume that for all positive t and for all bounded predictable processes H, the r.v.'s
converge in probability to a limit J(t, H) when n tends to infinity. Then there exists a semimartingale X such that, for all t and H, J(t, H)=
. 相似文献
9.
William M. McGovern 《Inventiones Mathematicae》1989,97(1):209-217
Summary LetG be a complex semisimple algebraic group with Lie algebra
. Let
be a nilpotentG-orbit,
its ring of regular functions. We derive a formula for
as aG-module and prove some partial results on
a cover of
. We then relate this formula to various existing multiplicity formulas forK-types in Harish-Chandra bimodules ofG.Supported by National Science Foundation Grant DMS-8505550 相似文献
10.
Hendrik Grundling 《Acta Appl Math》1997,46(2):107-145
Given an inductive limit group
where each
is locally compact, and a continuous two-cocycle
, we construct a C*-algebra
group algebra
is imbedded in its multiplier algebra
, and the representations of
are identified with the strong operator continuous
of G. If any of these representations are faithful, the above imbedding is faithful. When G is locally compact,
is precisely
, the twisted group algebra of G, and for these reasons we regard
in the general case as a twisted group algebra for G. Applying this construction to the CCR-algebra over an infinite dimensional symplectic space (S,\,B),we realise the regular representations as the representation space of the C*-algebra
, and show that pointwise continuous symplectic group actions on (S,\, B) produce pointwise continuous actions on
, though not on the CCR-algebra. We also develop the theory to accommodate and classify 'partially regular' representations, i.e. representations which are strong operator continuous on some subgroup H of G (of suitable type) but not necessarily on G, given that such representations occur in constrained quantum systems. 相似文献
11.
Dr. John Walsh 《Probability Theory and Related Fields》1970,14(3):169-188
Summary In this paper we treat a time-symmetrical Martin boundary theory for continuous parameter Markov chains. This is done by reversing the time sense of a Markov chainX
t
in such a way as to obtain a dual Markov chain
, and considering the two chains together. Various relations between the Martin exit boundaries
and
of these processes are studied. The exit boundary
of
, is in a sense an entrance boundary forX
t
and vice versa. After a natural identification of certain points in
and
one can topologizeI
in such a way thatboth X
t and
have standard modifications in this space which are right continuous, have left limits, and are strongly Markov.Research supported in part at Stanford University, Stanford, California under AFOSR 0049. 相似文献
12.
Let (G,
) denote a finite groupG with fibration
. The group Aut (G,
) of operators of (G,
) is closely related to the group of collineations of (G,
). In this paper we investigate the geometric properties imposed on (G,
) by requiring that Aut (G,
)=AutG. We find that in many instances this algebraic property restricts the geometry to a very special form.Dedicated to Professor Helmut Karzel on the occasion of his 60th birthday. 相似文献
13.
Scott McCullough 《Integral Equations and Operator Theory》2001,39(3):335-362
Let
denote an annulus,E a finite subset of
with at least three elements, and
the ideal of functions in
which vanish at the points ofE. The quotient
does not have a completely isometric representation on a finite dimensional Hilbert space. This complements a result of [11] which implies that the quotient has an isometric representation on a Hilbert space of dimension twice the cardinality ofE. 相似文献
14.
Johannes Schoissengeier 《Monatshefte für Mathematik》1992,114(2):139-147
A proof of the formula
for locally compact fields
andC
1-isomorphisms :UV, whereU andV are open subsets of
, was never published. In this paper we give two short proofs, one of them is a more elementary variant of the other. 相似文献
15.
LetT be a contraction acting in a separable Hilbert space
and leaving invariant a nest
of subspaces of
. We answer the question: when doesT have an isometric extension to
which leaves invariant the nest
= {N N :N
;}. 相似文献
16.
Edgar R. Lorch 《Integral Equations and Operator Theory》1981,4(3):422-434
The objects studied are the subalgebras of
which contain co. These are isometrically isomorphic to the algebras C(
) where
is a compactification of a discrete denumerable set N . It is shown: 1) If
is metric then there is a projection of norm 1, P: C(
) C(
) with kernel co defined by PF = f o where is a retraction of
onto
=
– N . 2) If
is metric, then the group of homeomorphisms of
is isomorphic to a complete group of permutations of the natural numbers . 3) The group of homeomorphisms of a compact metric space is the homomorphic image of a complete group of permutations of ("complete" means "no outer automorphisms, trivial center"). 相似文献
17.
V. Koubek 《Algebra Universalis》1996,35(2):296-331
Given distinct varieties
and
of the same type, we say that
is relatively
-universal if there exists an embedding :K
from a universal categoryK such that for every pairA, B ofK-objects, a homomorphismf:A B has the formf=g for someK-morphismg:A B if and only if Im(f)
. Finitely generated relatively
-universal varieties of Heyting algebras are described for the variety
of Boolean algebras, the variety generated by a three element chain, and for the variety generated by the four element Boolean algebra with an added greatest element.Dedicated to the memory of Alan DayPresented by J. Sichler.The support of the NSERC is gratefully acknowledged. 相似文献
18.
Necdet Güner 《Geometriae Dedicata》1996,63(1):17-23
Let N=G/ be a compact nilmanifold, G a connected, simply connected, nilpotent Lie group with its discrete subgroup and Lie algebra
. Let I* (
) denote the invariant differential forms on
.If I* (
) H* (
) is an injective map, then G is abelian and N is a torus. Furthermore, N has a formal minimal model. If N is an even-dimensional compact nilmanifold, it has a Kähler structure and invariant symplectic structure if and only if I* (
) H* (
) is injective. 相似文献
19.
A renormalization group transformation R
1 has a single stable point
in the space of the analytic circle homeomorphisms with a single cubic critical point and with the rotation number
(the golden mean). Let a homeomorphism T be the C
1-conjugate of
. We let
denote the sequence of distribution functions of the time of the kth entrance to the nth renormalization interval for the homeomorphism T. We prove that for any
, the sequence
has a finite limiting distribution function
, which is continuous in
, and singular on the interval [0,1]. We also study the sequence
for k>1. 相似文献
20.
We consider the extremal problem to determine the maximal number
of columns of a 0-1 matrix with
rows and at most
ones in each column such that each
columns are linearly independent modulo
. For fixed integers
and
, we shall prove the probabilistic lower bound
=
; for
a power of
, we prove the upper bound
which matches the lower bound for infinitely many values of
. We give some explicit constructions. 相似文献