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1.
V. G. Bardakov 《Acta Appl Math》2005,85(1-3):41-48
In this paper we prove that the braid group Bn(S2) of 2-sphere, mapping class group M(0,n) of the n-punctured 2-sphere and the braid group B3(P2) of the projective plane are linear.
Partially supported by the Russian Foundation for Basic Research (grant number 02-01-01118).Mathematics Subject Classifications (2000) 20F28, 20F36, 20G35. 相似文献
2.
Guglielmo Lunardon 《Geometriae Dedicata》1986,20(2):121-131
Summary In this paper, for q even, we construct an ovoid O
3 and a spread S of the finite classical polar space Q+(7, q) determinated by a hyperbolic quadric Q+ of PG(7, q) such that there is a subgroup of PGO
+
8
(q) isomorphic to PGL2(q
3), which maps O
3 in itself and S in S and is 3-transitive on O
3 and on S; for q>2, S is not a Desarguesian spread of Q+(7, q) and O
3 is a Desarguesian ovoid.
Al Prof. Adriano Barlotti in occasione del suo 60o compleanno 相似文献
Varietà di Segre e ovoidi dello spazio polare Q+(7, q)
Al Prof. Adriano Barlotti in occasione del suo 60o compleanno 相似文献
3.
We introduce the notion of even Clifford structures on Riemannian manifolds, which for rank r=2 and r=3 reduce to almost Hermitian and quaternion-Hermitian structures respectively. We give the complete classification of manifolds carrying parallel rank r even Clifford structures: Kähler, quaternion-Kähler and Riemannian products of quaternion-Kähler manifolds for r=2,3 and 4 respectively, several classes of 8-dimensional manifolds (for 5?r?8), families of real, complex and quaternionic Grassmannians (for r=8,6 and 5 respectively), and Rosenfeld?s elliptic projective planes OP2, (C⊗O)P2, (H⊗O)P2 and (O⊗O)P2, which are symmetric spaces associated to the exceptional simple Lie groups F4, E6, E7 and E8 (for r=9,10,12 and 16 respectively). As an application, we classify all Riemannian manifolds whose metric is bundle-like along the curvature constancy distribution, generalizing well-known results in Sasakian and 3-Sasakian geometry. 相似文献
4.
Let L be a restricted Lie algebra. The symmetric algebra Sp(L) of the restricted enveloping algebra u(L) has the structure of a Poisson algebra. We give necessary and sufficient conditions on L in order for the symmetric algebra Sp(L) to satisfy a multilinear Poisson identity. We also settle the same problem for the symmetric algebra S(L) of a Lie algebra L over an arbitrary field.
The first author was partially supported by MIUR of Italy. The second author was partially supported by Grant RFBR-04-01-
00739.
Received: 31 October 2005 相似文献
5.
The Lie module of the group algebra
F\mathfrakSn{{F\mathfrak{S}_n}} of the symmetric group is known to be not projective if and only if the characteristic p of F divides n. We show that in this case its non-projective summands belong to the principal block of
F\mathfrakSn{{F\mathfrak{S}_n}} . Let V be a vector space of dimension m over F, and let L
n
(V) be the n-th homogeneous part of the free Lie algebra on V; this is a polynomial representation of GL
m
(F) of degree n, or equivalently, a module of the Schur algebra S(m, n). Our result implies that, when m ≥ n, every summand of L
n
(V) which is not a tilting module belongs to the principal block of S(m, n), by which we mean the block containing the n-th symmetric power of V. 相似文献
6.
Baohua Fu 《Inventiones Mathematicae》2003,151(1):167-186
In this paper, firstly we calculate Picard groups of a nilpotent orbit 𝒪 in a classical complex simple Lie algebra and discuss
the properties of being ℚ-factorial and factorial for the normalization 𝒪tilde; of the closure of 𝒪. Then we consider the
problem of symplectic resolutions for 𝒪tilde;. Our main theorem says that for any nilpotent orbit 𝒪 in a semi-simple complex
Lie algebra, equipped with the Kostant-Kirillov symplectic form ω, if for a resolution π:Z𝒪tilde;, the 2-form π*(ω) defined on π−1(𝒪) extends to a symplectic 2-form on Z, then Z is isomorphic to the cotangent bundle T
*(G/P) of a projective homogeneous space, and π is the collapsing of the zero section. It proves a conjecture of Cho-Miyaoka-Shepherd-Barron
in this special case. Using this theorem, we determine all varieties 𝒪tilde; which admit such a resolution.
Oblatum 6-V-2002 & 7-VIII-2002?Published online: 10 October 2002 相似文献
7.
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(
n
n+x
). Here we prove that the order x Veronese embedding ofP
n
is not weakly (k−1)-defective, i.e. for a general S⊃P
n
such that #(S) = k+1 the projective space | I
2S
(x)| of all degree t hypersurfaces ofP
n
singular at each point of S has dimension (
n
/n+x
)−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I
2S
(x)| has an ordinary double point at each P∈ S and Sing (F)=S.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
8.
Robert Wisbauer 《代数通讯》2013,41(7):2683-2711
Generalizing the notion of Galois corings, Galois comodules were introduced as comodules P over an A-coring 𝒞 for which P A is finitely generated and projective and the evaluation map μ𝒞:Hom 𝒞 (P, 𝒞) ? S P → 𝒞 is an isomorphism (of corings) where S = End 𝒞 (P). It has been observed that for such comodules the functors ? ? A 𝒞 and Hom A (P, ?) ? S P from the category of right A-modules to the category of right 𝒞-comodules are isomorphic. In this note we use this isomorphism related to a comodule P to define Galois comodules without requiring P A to be finitely generated and projective. This generalises the old notion with this name but we show that essential properties and relationships are maintained. Galois comodules are close to being generators and have common properties with tilting (co)modules. Some of our results also apply to generalised Hopf Galois (coalgebra Galois) extensions. 相似文献
9.
Summary A projectively normal subvariety (X,O
X) ofP
N(k), k an algebraically closed field of characteristic zero, will be said to be projectively almost-factorial if each Weil
divisor has a multiple which is a complete intersection in X. The main result is the following: (X,O
X) is projectively almost-factorial if and only if for all x ∈ X the local ringO
x is almost-factorial and the quotient ofPic(X) modulo the subgroup generated by the class ofO
X
(1) is torsion. We also prove the invariance of the projective almost-factoriality up to isomorphisms and state some relations
between the projective almost-factoriality (resp. projective factoriality) of X and the almost-factoriality (resp. factoriality)
of the affine open subvarieties. Finally we discuss some consequences of the main result in the case k=ℂ: in particular we prove that the Picard group of a projectively almost-factorial variety is isomorphic to the Néron-Severi
group, hence finitely generated.
Entrata in Redazione il 23 aprile 1976.
AMS(MOS) subject classification (1970): Primary 14C20, 13F15. 相似文献
10.
V. V. Makeev 《Journal of Mathematical Sciences》2011,175(5):562-568
Let
g23:E2( \mathbbR3 ) ? G2( \mathbbR3 ) \gamma_2^3:{E_2}\left( {{\mathbb{R}^3}} \right) \to {G_2}\left( {{\mathbb{R}^3}} \right) be the tautological vector bundle over the Grassmann manifold of 2-planes in
\mathbbR3 {\mathbb{R}^3} , where the fiber over a plane is the plane itself regarded as a two-dimensional subspace of
\mathbbR3 {\mathbb{R}^3} . A field of convex figures is given in γ23 if a convex figure is distinguished in each fiber so that the figure continuously depends on the fiber. It is proved that
each field of convex figures in γ23 contains a figure K containing a centrally symmetric convex figure of area ( 4 + 16?2 ) \left( {4 + 16\sqrt {2} } \right)
S(K)/31 > 0.858 S(K) (S(K) denotes the area of K), and a figure K′ that is contained in a centrally symmetric convex figure of area ( 12?2 - 8 ) \left( {12\sqrt {2} - 8} \right)
S(K′)/7 < 1.282 S(K′). It is also proved that each three-dimensional convex body K is contained in a centrally symmetric convex cylinder of volume ( 36?2 - 24 ) \left( {36\sqrt {2} - 24} \right)
V(K)/7 < 3.845 V(K). (Here, V(K) denotes the volume of K.) Bibliography: 5 titles. 相似文献
11.
N. G. Chebochko 《代数通讯》2017,45(7):2969-2977
All classes of integrable cocycles in H2(L,L) are obtained for Lie algebra of type G2 over an algebraically closed field of characteristic 2. It is proved that there exist only two orbits of classes of integrable cocycles with respect to automorphism group. The global deformation is shown to exist for any nontrivial class of integrable cocycles. These deformations are isomorphic to one of the two algebras of Cartan type, one of which being S(3:1,ω) while the other H(4:1,ω). 相似文献
12.
Jianwei Zhou 《Acta Mathematica Hungarica》2006,111(1-2):29-41
Summary We study minimal and totally geodesic submanifolds in Lie groups and related problems. We show that: (1) The imbedding of
the Grassmann manifold GF(n,N) in the Lie group GF(N) defined naturally makes GF(n,N) a totally geodesic submanifold; (2) The imbedding S7→SO(8) defined by octonians makes S7a totally geodesic submanifold inSO(8); (3) The natural inclusion of the Lie group GF(N) in the sphere ScN^2-1(√N) of gl(N,F)is minimal. Therefore the natural imbedding GF(N)<span style='font-size:10.0pt;font-family:"Lucida Sans Unicode"'>→gl(N,F)is formed by the eigenfunctions of the Laplacian on GF(N). 相似文献
13.
Sergiy Maksymenko 《Annals of Global Analysis and Geometry》2006,29(3):241-285
Let M be a smooth compact surface, orientable or not, with boundary or without it, P either the real line ℝ
1 or the circle S
1, and D(M) the group of diffeomorphisms of M acting on C^∞(M, P) by the rule h⋅ f = f ∘ h
−1 for h ∊ D(M) and f ∊ C^∞ (M,P). Let f: M → P be an arbitrary Morse mapping, Σ
f
the set of critical points of f, D(M,Σ
f
) the subgroup of D(M) preserving Σ
f
, and S(f), S (f,Σ
f
), O(f), and O(f,Σ
f
) the stabilizers and the orbits of f with respect to D(M) and D(M,Σ
f
). In fact S(f) = S(f,Σ
f
).In this paper we calculate the homotopy types of S(f), O(f) and O(f,Σ
f
). It is proved that except for few cases the connected components of S(f) and O(f,Σ
f
) are contractible, π
k
O(f) = π
k
M for k ≥ 3, π2 O(f) = 0, and π1 O(f) is an extension of π1 D(M) ⊕ Z
k
(for some k ≥ 0) with a (finite) subgroup of the group of automorphisms of the Kronrod-Reeb graph of f.We also generalize the methods of F. Sergeraert to give conditions for a finite codimension orbit of a tame smooth action of a tame Lie group on a tame Fréchet manifold to be a tame Fréchet manifold itself. In particular, we obtain that O(f) and O(f, Σ
f
) are tame Fréchet manifolds.
Communicated by Peter Michor Vienna
Mathematics Subject Classifications (2000): 37C05, 57S05, 57R45. 相似文献
14.
Let X be a smooth irreducible
non-degenerated projective curve in some projective space PN. Let
r be a positive integer such that 2r + 1 < N
and let Sr(X) be the r-th secant
variety of X. It is a variety of dimension
2r + 1. In this paper we prove that the singular locus is the (r - 1)-th secant
variety Sr- 1(X) if X does not have
any (2r + 2)-secant 2r-space divisor.
Received: 26 November 2002 相似文献
15.
Otto Röschel 《Journal of Geometry》1992,44(1-2):160-170
We study a map of osculating elements of an affine Cayley- Klein (CK-) plane into the Lie algebraA
4(2) of the aequiform transformationsA
4(2) of the given plane. If we use the real projective spaceP
3() overA
4(2) each osculating element defines a straight line inP
3(). In the first part of this paper this map is studied in detail. In the second part we study second order properties of one- parameter motions and their corresponding properties in the Lie algebraA
4(2). This is done by considering the analogen to the formula of EULERSAVARY in the image spaceP
3() overA
4(2). 相似文献
16.
We give a presentation of the Schur algebras S
Q
(2,d) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the process we find a new basis for S
Q
(2,d), a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis. 相似文献
17.
ABSTRACT Rank 2-amalgams (P 1, P 2, B), in which P 1/O 2(P 1) ? P 2/O 2(P 2) ? S 5, are analyzed using the amalgam method. It is determined that in the noncommuting case either |O 2(P 1)| = |O 2(P 2)| ≤ 26 or (P 1, P 2, B) has the same shape as an amalgam in Aut(G 2(4)). 相似文献
18.
Let S be a smooth projective surface over C polarized by a 2-very ample line bundle L=O
S(L), i.e. for any 0-dimensional subscheme (Z,O
Z
) of length 3 the restriction map Γ(L)→Γ(L⊗O
Z) is a surjection. This generalization of very ampleness was recently introduced by M. Beltrametti and A.J. Sommese.
The authors prove that, if L·L≥13, the adjoint line bundleK
S⊗L is 2-very ample apart from a list of well understood exceptions and up to contracting down the smooth rational curves E such
that E·E=−1, L·E=2.
The appendix contains an inductive argument in order to extend the result in higher dimension. 相似文献
19.
We show that if a smooth projective 4-fold M contains an ample divisor A which is P
1-bundle π :A→S over a smooth projective surface S, π is extended to a P
2-bundle π :S→S, unless $A$ is isomorphic to P
2×P
1.
Received: 28 September 1998 / Revised version: 16 August 1999 相似文献
20.
Jie Du 《manuscripta mathematica》1992,75(1):411-427
The structure of Schur algebrasS(2,r) over the integral domainZ is intensively studied from the quasi-hereditary algebra point of view. We introduce certain new bases forS(2,r) and show that the Schur algebraS(2,r) modulo any ideal in the defining sequence is still such a Schur algebra of lower degree inr. A Wedderburn-Artin decomposition ofS
K
(2,r) over a fieldK of characteristic 0 is described. Finally, we investigate the extension groups between two Weyl modules and classify the
indecomposable Weyl-filtered modules for the Schur algebrasS
Zp(2,r) withr<p
2
.
Research supported by ARC Large Grant L20.24210 相似文献