共查询到20条相似文献,搜索用时 15 毫秒
1.
A two-point set is a subset of the plane which meets every line in exactly two points. We discuss previous work on the topological symmetries of a two-point set, and show that there exist subgroups of S1 which do not leave any two-point set invariant. Further, we show that two-point sets may be chosen to be topological groups, in which case they are also homogeneous. 相似文献
2.
Yoshio Agaoka 《Proceedings of the American Mathematical Society》2001,129(9):2753-2762
We show the uniqueness of left invariant symplectic structures on the affine Lie group under the adjoint action of , by giving an explicit formula of the Pfaffian of the skew symmetric matrix naturally associated with , and also by giving an unexpected identity on it which relates two left invariant symplectic structures. As an application of this result, we classify maximum rank left invariant Poisson structures on the simple Lie groups and . This result is a generalization of Stolin's classification of constant solutions of the classical Yang-Baxter equation for and .
3.
The study of the Lie groups with a left invariant flat pseudo-metric is equivalent to the study of the left-symmetric algebras
with a nondegenerate left invariant bilinear form. In this paper, we consider such a structure satisfying an additional condition
that there is a decomposition into a direct sum of the underlying vector spaces of two isotropic subalgebras. Moreover, there
is a new underlying algebraic structure, namely, a special L-dendriform algebra and then there is a bialgebra structure which
is equivalent to the above structure. The study of coboundary cases leads to a construction from an analogue of the classical
Yang–Baxter equation. 相似文献
4.
André Diatta 《Differential Geometry and its Applications》2008,26(5):544-552
Amongst other results, we perform a ‘contactization’ method to construct, in every odd dimension, many contact Lie groups with a discrete center, unlike the usual (classical) contactization which only produces Lie groups with a non-discrete center. We discuss some applications and consequences of such a construction, construct several examples and derive some properties. We give classification results in low dimensions. A complete list is supplied in dimension 5. In any odd dimension greater than 5, there are infinitely many locally non-isomorphic solvable contact Lie groups. We also characterize solvable contact Lie algebras whose derived ideal has codimension one. For simplicity, most of the results are given in the Lie algebra version. 相似文献
5.
《Mathematische Nachrichten》2017,290(14-15):2341-2355
In this paper, we use the powerful tool Milnor bases to determine all the locally symmetric left invariant Riemannian metrics up to automorphism, on 3‐dimensional connected and simply connected Lie groups, by solving system of polynomial equations of constants structure of each Lie algebra . Moreover, we show that E 0(2) is the only 3‐dimensional Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric. 相似文献
6.
7.
Lorenz J. Schwachhöfer 《Archiv der Mathematik》2008,90(2):158-162
We show that a left invariant metric on a compact Lie group G with Lie algebra has some negative sectional curvature if it is obtained by enlarging a biinvariant metric on a subalgebra , unless the semi-simple part of is an ideal of This answers a question raised in [8].
Received: 7 May 2007 相似文献
8.
Let G be a Lie group, T*G=Lie(G)*G its cotangent bundle considered as a Lie group, where G acts on Lie(G)* via the coadjoint action. Each solution r of the Classical Yang Baxter Equation on G, corresponds to a connected Lie subgroup H of T*G such that Lie(H) is a Lagrangian graph in Lie(G)Lie(G)* and H carries a left invariant affine structure. If r is invertible, the Poisson Lie tensor given by r on G is polynomial of degree at most 2 and every double Lie group of (G,) is endowed with an affine and a complex structures and J, both left invariant and given by r, such that J=0.Mathematics Subject Classification (2000): 53D17, 53A15, 17B62Acknowledgements. The first author was partially supported by Enterprise Ireland. He wishes to thank the mathematical department of NUI Maynooth for their kind welcome, during his stay.Revised version: 5 April 2004 相似文献
9.
Yoshio Agaoka 《Israel Journal of Mathematics》2000,116(1):189-222
A Poisson structure on a Lie group is called left invariant if the contravariant 2-tensor field π corresponding to the Poisson
structure is left invariant. Explicit examples of such structures were known only for few cases, and in this paper, we give
new examples of high rank left invariant Poisson structures for all non-compact classical real simple Lie groups. This result
is equivalent to give constant solutions of the classical Yang-Baxter equation [r
12,r
13]+[r
12,r
23]+[r
13,r
23]=0 taking values in the space ^2g for these Lie groups. 相似文献
10.
11.
Edoardo Ballico 《Annals of Global Analysis and Geometry》1995,13(3):227-230
Here we classify projective 3-folds with a holomorphic flat projective structure and Kodaira dimension 1 or 2.The author was partially supported by MURST and GNSAGA of CNR (Italy). 相似文献
12.
We study left invariant contact forms and left invariant symplectic forms on Lie groups. In the case of filiform Lie groups we give a necessary and sufficient condition for the existence of a left invariant contact form and we prove the uniqueness of this contact form up to a nonzero scalar multiple. As an application we classify all symplectic structures on nilpotent Lie algebras of dimension ?6. 相似文献
13.
Isabel Dotti Miatello 《Mathematische Zeitschrift》1982,180(3):257-263
14.
Abdelghani Zeghib 《Mathematische Zeitschrift》1998,227(2):245-262
15.
Thomas Binder 《Abhandlungen aus dem Mathematischen Seminar der Universit?t Hamburg》2009,79(2):265-281
The study of affine differential geometry is partially motivated by the fact that the direction of the affine normal coincides
with the tangent direction of the gravity curve at the base point. A way to prove this is to compute the Taylor expansion
of the hypersurface up to third order derivatives. By computing fourth and fifth order coefficients we characterize the second
order behavior of the gravity curve at its base point in terms of affine invariants. 相似文献
16.
Hirohiko Shima 《Transactions of the American Mathematical Society》1999,351(12):4713-4726
We characterize invariant projectively flat affine connections in terms of affine representations of Lie algebras, and show that a homogeneous space admits an invariant projectively flat affine connection if and only if it has an equivariant centro-affine immersion. We give a correspondence between semi-simple symmetric spaces with invariant projectively flat affine connections and central-simple Jordan algebras.
17.
We classify the 6-dimensional Lie algebras of the form that admit an integrable complex structure. We also endow a Lie algebra of the kind () with such a complex structure. The motivation comes from geometric structures à la Sasaki on -manifolds. 相似文献
18.
For each simply connected three‐dimensional Lie group we determine the automorphism group, classify the left invariant Riemannian metrics up to automorphism, and study the extent to which curvature can be altered by a change of metric. Thereby we obtain the principal Ricci curvatures, the scalar curvature and the sectional curvatures as functions of left invariant metrics on the three‐dimensional Lie groups. Our results improve a bit of Milnor's results of [7] in the three‐dimensional case, and Kowalski and Nikv?cevi?'s results [6, Theorems 3.1 and 4.1] (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
19.
A. R. Chekhlov 《Journal of Mathematical Sciences》2010,164(1):143-147
The properties of projective invariant subgroups are studied. The structure of these subgroups in nonreduced groups is described.
The conditions under which projective invariant subgroups are fully invariant are considered. 相似文献
20.
Gabriel Picavet 《Journal of Pure and Applied Algebra》2002,174(2):163-185
We define and study algebraically flat algebras in order to have a better understanding of algebraically projective algebras of finite type (the projective algebras of literature). A close examination of the differential properties of these algebras leads to our main structure theorem. As a corollary, we get that an algebraically projective algebra of finite type over a field is either a polynomial ring or the affine algebra of a complete intersection. 相似文献