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1.
J. Bagherian Ilia Ponomarenko A. Rahnamai Barghi 《Journal of Algebraic Combinatorics》2008,27(2):173-185
We introduce a concept of cyclotomic association scheme over a finite near-field
. It is proved that any isomorphism of two such nontrivial schemes is induced by a suitable element of the group AGL(V), where V is the linear space associated with
. A sufficient condition on a cyclotomic scheme
that guarantee the inclusion
where
is a finite field with
elements, is given.
I. Ponomarenko partially supported by RFFI, grants 03-01-00349, NSH-2251.2003.1. 相似文献
2.
Emanuele Delucchi 《Journal of Algebraic Combinatorics》2007,26(4):477-494
Given a finite group G and a natural number n, we study the structure of the complex of nested sets of the associated Dowling lattice
(Proc. Internat. Sympos., 1971, pp. 101–115) and of its subposet of the G-symmetric partitions
which was recently introduced by Hultman (, 2006), together with the complex of G-symmetric phylogenetic trees
. Hultman shows that the complexes
and
are homotopy equivalent and Cohen–Macaulay, and determines the rank of their top homology.
An application of the theory of building sets and nested set complexes by Feichtner and Kozlov (Selecta Math. (N.S.)
10, 37–60, 2004) shows that in fact
is subdivided by the order complex of
. We introduce the complex of Dowling trees
and prove that it is subdivided by the order complex of
. Application of a theorem of Feichtner and Sturmfels (Port. Math. (N.S.)
62, 437–468, 2005) shows that, as a simplicial complex,
is in fact isomorphic to the Bergman complex of the associated Dowling geometry.
Topologically, we prove that
is obtained from
by successive coning over certain subcomplexes. It is well known that
is shellable, and of the same dimension as
. We explicitly and independently calculate how many homology spheres are added in passing from
to
. Comparison with work of Gottlieb and Wachs (Adv. Appl. Math.
24(4), 301–336, 2000) shows that
is intimely related to the representation theory of the top homology of
.
Research partially supported by the Swiss National Science Foundation, project PP002-106403/1. 相似文献
3.
Dmitri I. Panyushev 《Transformation Groups》2009,14(2):463-482
Let be an algebraic Lie algebra and a (generalised) Takiff algebra. Any finite-order automorphism θ of induces an automorphism of of the same order, denoted . We study invariant-theoretic properties of representations of the fixed point subalgebra of on other eigenspaces of in . We use the observation that, for special values of m, the fixed point subalgebra, , turns out to be a contraction of a certain Lie algebra associated with and θ.
To my teacher
Supported in part by R.F.B.R. grant 06-01-72550. 相似文献
4.
Let be a commutative Noetherian local ring and let be an ideal of R. We give some inequalities between the Bass numbers of an R–module and those of its local cohomology modules with respect to . As an application of these inequalities, we recover results of Delfino-Marley and Kawasaki by showing that for a minimax
R-module M and for any non-negative integer i, the Bass numbers of the ith local cohomology module are finite if one of the following holds:
S. Yassemi was supported by a grant from IPM No. 85130214. 相似文献
(a) | , |
(b) | is a principal ideal. |
5.
6.
T. Skrypnyk 《Acta Appl Math》2007,99(3):261-282
We construct a family of special quasigraded Lie algebras
of functions of one complex variables with values in finite-dimensional Lie algebra
, labeled by the special 2-cocycles F on
. The main property of the constructed Lie algebras
is that they admit Kostant-Adler-Symes scheme. Using them we obtain new integrable finite-dimensional Hamiltonian systems
and new hierarchies of soliton equations. 相似文献
7.
Svante Linusson John Shareshian Volkmar Welker 《Journal of Algebraic Combinatorics》2008,27(3):331-349
For positive integers k,n, we investigate the simplicial complex
of all graphs G on vertex set [n] such that every matching in G has size less than k. This complex (along with other associated cell complexes) is found to be homotopy equivalent to a wedge of spheres. The
number and dimension of the spheres in the wedge are determined, and (partially conjectural) links to other combinatorially
defined complexes are described. In addition we study for positive integers r,s and k the simplicial complex
of all bipartite graphs G on bipartition
such that there is no matching of size k in G, and obtain results similar to those obtained for
.
S. Linusson and V. Welker supported by EC’s IHRP program through grant HPRN-CT-2001-00272. J. Shareshian partially supported
by National Science Foundation grants DMS-0070757 and DMS-0030483. 相似文献
8.
Let be a field and q be a nonzero element of that is not a root of unity. We give a criterion for 〈0〉 to be a primitive ideal of the algebra of quantum matrices. Next, we describe all height one primes of ; these two problems are actually interlinked since it turns out that 〈0〉 is a primitive ideal of whenever has only finitely many height one primes. Finally, we compute the automorphism group of in the case where m ≠ n. In order to do this, we first study the action of this group on the prime spectrum of . Then, by using the preferred basis of and PBW bases, we prove that the automorphism group of is isomorphic to the torus when m ≠ n and (m,n) ≠ (1, 3),(3, 1).
This research was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme
and by Leverhulme Research Interchange Grant F/00158/X. 相似文献
9.
Let be the scheme of the laws defined by the Jacobi identities on with a field. A deformation of , parametrized by a local ring A, is a local morphism from the local ring of at ϕ
m
to A. The problem of classifying all the deformation equivalence classes of a Lie algebra with given base is solved by “versal”
deformations. First, we give an algorithm for computing versal deformations. Second, we prove there is a bijection between
the deformation equivalence classes of an algebraic Lie algebra ϕ
m
= R ⋉ φ
n
in and its nilpotent radical φ
n
in the R-invariant scheme with reductive part R, under some conditions. So the versal deformations of ϕ
m
in are deduced from those of φ
n
in , which is a more simple problem. Third, we study versality in central extensions of Lie algebras. Finally, we calculate versal
deformations of some Lie algebras.
Supported by the EC project Liegrits MCRTN 505078. 相似文献
10.
A frame homomorphism h : A ⟶ B is skeletal if x
⊥⊥ = 1 in A implies that h(x)⊥⊥ = 1 in B. It is shown that, in , the category of compact regular frames with skeletal maps, the subcategory , consisting of the frames in which every polar is complemented, coincides with the epicomplete objects in . Further, is the least epireflective subcategory, and, indeed, the target of the monoreflection which assigns to a compact regular
frame A, the ideal frame ε A of , the boolean algebra of polars of A.
相似文献
11.
Tomoyuki Arakawa 《Inventiones Mathematicae》2007,169(2):219-320
We study the representation theory of the -algebra associated with a simple Lie algebra at level k. We show that the “-” reduction functor is exact and sends an irreducible module to zero or an irreducible module at any
level k∈ℂ. Moreover, we show that the character of each irreducible highest weight representation of is completely determined by that of the corresponding irreducible highest weight representation of affine Lie algebra of . As a consequence we complete (for the “-” reduction) the proof of the conjecture of E. Frenkel, V. Kac and M. Wakimoto on
the existence and the construction of the modular invariant representations of -algebras.
Mathematics Subject Classification (1991) 17B68, 81R10 相似文献
12.
In this article, we use a discrete Calderón-type reproducing formula and Plancherel-Pôlya-type inequality associated to a para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type $\dot{F}^{\alpha,q}_{b,p}In this article, we use a discrete Calderón-type reproducing formula and Plancherel-P?lya-type inequality associated to a
para-accretive function to characterize the Triebel-Lizorkin spaces of para-accretive type
, which reduces to the classical Triebel-Lizorkin spaces when the para-accretive function is constant. Moreover, we give a
necessary and sufficient condition for the
boundedness of paraproduct operators. From this, we show that a generalized singular integral operator T with M
b
TM
b
∈WBP is bounded from
to
if and only if
and T
*
b=0 for
, where ε is the regularity exponent of the kernel of T.
Chin-Cheng Lin supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-008-021-MY3.
Kunchuan Wang supported by National Science Council, Republic of China under Grant #NSC 97-2115-M-259-009 and NCU Center for
Mathematics and Theoretic Physics. 相似文献
13.
14.
Given a set of points
and ε>0, we propose and analyze an algorithm for the problem of computing a (1+ε)-approximation to the minimum-volume axis-aligned ellipsoid enclosing
. We establish that our algorithm is polynomial for fixed ε. In addition, the algorithm returns a small core set
, whose size is independent of the number of points m, with the property that the minimum-volume axis-aligned ellipsoid enclosing
is a good approximation of the minimum-volume axis-aligned ellipsoid enclosing
. Our computational results indicate that the algorithm exhibits significantly better performance than the theoretical worst-case
complexity estimate.
This work was supported in part by the National Science Foundation through CAREER Grants CCF-0643593 and DMI-0237415. 相似文献
15.
We obtain the decomposition of the tensor space
as a module for
, find an explicit formula for the multiplicities of its irreducible summands, and (when n 2k) describe the centralizer algebra
=
(
) and its representations. The multiplicities of the irreducible summands are derangement numbers in several important instances, and the dimension of
is given by the number of derangements of a set of 2k elements. 相似文献
16.
Let be a finite-dimensional complex reductive Lie algebra and S() its symmetric algebra. The nilpotent bicone of is the subset of elements (x, y) of whose subspace generated by x and y is contained in the nilpotent cone. The nilpotent bicone is naturally endowed with a scheme structure, as nullvariety of
the augmentation ideal of the subalgebra of generated by the 2-order polarizations of invariants of . The main result of this paper is that the nilpotent bicone is a complete intersection of dimension , where and are the dimensions of Borel subalgebras and the rank of , respectively. This affirmatively answers a conjecture of Kraft and Wallach concerning the nullcone [KrW2]. In addition, we introduce and study in this paper the characteristic submodule of . The properties of the nilpotent bicone and the characteristic submodule are known to be very important for the understanding
of the commuting variety and its ideal of definition. The main difficulty encountered for this work is that the nilpotent
bicone is not reduced. To deal with this problem, we introduce an auxiliary reduced variety, the principal bicone. The nilpotent bicone, as well as the principal bicone, are linked to jet schemes. We study their dimensions using arguments
from motivic integration. Namely, we follow methods developed by Mustaţǎ in [Mu]. Finally, we give applications of our results to invariant theory. 相似文献
17.
Hideo Mitsuhashi 《Algebras and Representation Theory》2006,9(3):309-322
In this paper, we establish Schur–Weyl reciprocity between the quantum general super Lie algebra and the Iwahori–Hecke algebra . We introduce the sign -permutation representation of on the tensor space of dimensional -graded -vector space . This action commutes with that of derived from the vector representation on . Those two subalgebras of satisfy Schur–Weyl reciprocity. As special cases, we obtain the super case (), and the quantum case (). Hence this result includes both the super case and the quantum case, and unifies those two important cases.Presented by A. Verschoren. 相似文献
18.
Michael Taylor 《Journal of Geometric Analysis》2009,19(1):137-190
We develop the theory of the “local” Hardy space
and John-Nirenberg space
when M is a Riemannian manifold with bounded geometry, building on the classic work of Fefferman-Stein and subsequent material,
particularly of Goldberg and Ionescu. Results include
–
duality, L
p
estimates on an appropriate variant of the sharp maximal function,
and bmo-Sobolev spaces, and action of a natural class of pseudodifferential operators, including a natural class of functions
of the Laplace operator, in a setting that unifies these results with results on L
p
-Sobolev spaces. We apply results on these topics to some interpolation theorems, motivated in part by the search for dispersive
estimates for wave equations.
相似文献
19.
Béla Bajnok 《Journal of Algebraic Combinatorics》2007,25(4):375-397
The hyperoctahedral group H in n dimensions (the Weyl group of Lie type B
n
) is the subgroup of the orthogonal group generated by all transpositions of coordinates and reflections with respect to coordinate
hyperplanes.With e
1
, ..., e
n
denoting the standard basis vectors of
n
and letting x
k
= e
1
+ ··· + e
k
(k = 1, 2, ..., n), the set
is the vertex set of a generalized regular hyperoctahedron in
n
.
A finite set with a weight function is called a Euclidean t-design, if
holds for every polynomial f of total degree at most t; here R is the set of norms of the points in ,W
r
is the total weight of all elements of with norm r, S
r
is the n-dimensional sphere of radius r centered at the origin, and is the average of f over S
r
.
Here we consider Euclidean designs which are supported by orbits of the hyperoctahedral group. Namely, we prove that any Euclidean
design on a union of generalized hyperoctahedra has strength (maximum t for which it is a Euclidean design) equal to 3, 5, or 7.We find explicit necessary and sufficient conditions for when this
strength is 5 and for when it is 7.In order to establish our classification, we translate the above definition of Euclidean
designs to a single equation for t = 5, a set of three equations for t = 7, and a set of seven equations for t = 9.
Neumaier and Seidel (1988), as well as Delsarte and Seidel (1989), proved a Fisher-type inequality for the minimum size of a Euclidean t-design in
n
on p = |R| concentric spheres (assuming that the design is antipodal if t is odd).A Euclidean design with exactly N (n, p, t) points is called tight. We exhibit new examples of antipodal tight Euclidean designs, supported by orbits of the hyperoctahedral
group, for N(n, p, t) = (3, 2, 5), (3, 3, 7), and (4, 2, 7). 相似文献
20.
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