共查询到20条相似文献,搜索用时 31 毫秒
1.
Jiantao Li 《Czechoslovak Mathematical Journal》2018,68(3):657-660
Free Poisson algebras are very closely connected with polynomial algebras, and the Poisson brackets are used to solve many problems in affine algebraic geometry. In this note, we study Poisson derivations on the symplectic Poisson algebra, and give a connection between the Jacobian conjecture with derivations on the symplectic Poisson algebra. 相似文献
2.
Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article, the noncommutative Poisson algebra structures on sp2e(~CQ) are determined. 相似文献
3.
4.
M. Boucetta 《Differential Geometry and its Applications》2004,20(3):279-291
In a previous paper (C. R. Acad. Sci. Paris Sér. I 333 (2001) 763–768), the author introduced a notion of compatibility between a Poisson structure and a pseudo-Riemannian metric. In this paper, we introduce a new class of Lie algebras called pseudo-Riemannian Lie algebras. The two notions are closely related: we prove that the dual of a Lie algebra endowed with its canonical linear Poisson structure carries a compatible pseudo-Riemannian metric if and only if the Lie algebra is a pseudo-Riemannian Lie algebra. Moreover, the Lie algebra obtained by linearizing at a point a Poisson manifold with a compatible pseudo-Riemannian metric is a pseudo-Riemannian Lie algebra. We also give some properties of the symplectic leaves of such manifolds, and we prove that every Poisson manifold with a compatible Riemannian metric is unimodular. Finally, we study Poisson Lie groups endowed with a compatible pseudo-Riemannian metric, and we give the classification of all pseudo-Riemannian Lie algebras of dimension 2 and 3. 相似文献
5.
Stefan Waldmann 《Bulletin of the Brazilian Mathematical Society》2011,42(4):831-852
Various aspects of Morita theory of deformed algebras and in particular of star product algebras on general Poisson manifolds
are discussed. We relate the three flavours ring-theoretic Morita equivalence, *-Morita equivalence, and strong Morita equivalence
and exemplify their properties for star product algebras. The complete classification of Morita equivalent star products on
general Poisson manifolds is discussed as well as the complete classification of covariantly Morita equivalent star products
on a symplectic manifold with respect to some Lie algebra action preserving a connection. 相似文献
6.
Noncommutative Poisson algebras are the algebras having both an associative algebra structure and a Lie algebra structure together with the Leibniz law. In this article,the noncommutative Poisson algebra structures on sp2l(^~CQ) are determined. 相似文献
7.
José M. Casas Tamar Datuashvili Manuel Ladra 《Central European Journal of Mathematics》2014,12(1):57-78
The notions of left-right noncommutative Poisson algebra (NPlr-algebra) and left-right algebra with bracket AWBlr are introduced. These algebras are special cases of NLP-algebras and algebras with bracket AWB, respectively, studied earlier. An NPlr-algebra is a noncommutative analogue of the classical Poisson algebra. Properties of these new algebras are studied. In the categories AWBlr and NPlr-algebras the notions of actions, representations, centers, actors and crossed modules are described as special cases of the corresponding wellknown notions in categories of groups with operations. The cohomologies of NPlr-algebras and AWBlr (resp. of NPr-algebras and AWBr) are defined and the relations between them and the Hochschild, Quillen and Leibniz cohomologies are detected. The cases P is a free AWBr, the Hochschild or/and Leibniz cohomological dimension of P is ≤ n are considered separately, exhibiting interesting possibilities of representations of the new cohomologies by the well-known ones and relations between the corresponding cohomological dimensions. 相似文献
8.
Hochschild cohomology governs deformations of algebras, and its graded Lie structure plays a vital role. We study this structure for the Hochschild cohomology of the skew group algebra formed by a finite group acting on an algebra by automorphisms. We examine the Gerstenhaber bracket with a view toward deformations and developing bracket formulas. We then focus on the linear group actions and polynomial algebras that arise in orbifold theory and representation theory; deformations in this context include graded Hecke algebras and symplectic reflection algebras. We give some general results describing when brackets are zero for polynomial skew group algebras, which allow us in particular to find noncommutative Poisson structures. For abelian groups, we express the bracket using inner products of group characters. Lastly, we interpret results for graded Hecke algebras. 相似文献
9.
Maysam Maysami Sadr 《Czechoslovak Mathematical Journal》2017,67(1):97-121
We define algebraic families of (all) morphisms which are purely algebraic analogs of quantum families of (all) maps introduced by P. M. So?tan. Also, algebraic families of (all) isomorphisms are introduced. By using these notions we construct two classes of Hopf-algebras which may be interpreted as the quantum group of all maps from a finite space to a quantum group, and the quantum group of all automorphisms of a finite noncommutative (NC) space. As special cases three classes of NC objects are introduced: quantum group of gauge transformations, Pontryagin dual of a quantum group, and Galois-Hopf-algebra of an algebra extension. 相似文献
10.
非交换的Poisson代数同时具有结合代数和李代数两种代数结构,而结合代数和李代数之间满足所谓的Leibniz法则.文中确定了Toroidal李代数上所有的Poisson代数结构,推广了仿射Kac-Moody代数上相应的结论. 相似文献
11.
The affine and degenerate affine Birman–Murakami–Wenzl (BMW) algebras arise naturally in the context of Schur–Weyl duality for orthogonal and symplectic quantum groups and Lie algebras, respectively. Cyclotomic BMW algebras, affine and cyclotomic Hecke algebras, and their degenerate versions are quotients of the affine and degenerate affine BMW algebras. In this paper, we explain how the affine and degenerate affine BMW algebras are tantalizers (tensor power centralizer algebras) by defining actions of the affine braid group and the degenerate affine braid algebra on tensor space and showing that, in important cases, these actions induce actions of the affine and degenerate affine BMW algebras. We then exploit the connection to quantum groups and Lie algebras to determine universal parameters for the affine and degenerate affine BMW algebras. Finally, we show that the universal parameters are central elements—the higher Casimir elements for orthogonal and symplectic enveloping algebras and quantum groups. 相似文献
12.
Alberto Elduque 《代数通讯》2013,41(6):3009-3030
Associated to any eight-dimensional non-unital composition algebra with associative norm, there are outer automorphisms of order 3 of the corresponding spin group, such tiat the fixed subgroup is the automorphism group of the composition algebra. Over fields of characteristic ≠ 3 these are simple algebraic groups of types G 2 or A 2, related respectively to the para-octonion and the Okubo algebras A connection between the Okubo algebras over fields of characteristic 3 with some simple noncommutative Jordan algebras will be used to compute explicitly the automorphism groups and Lie algebras of derivations of these algebras. In contrast to the other characteristics, ths groups will no longer be of type A 2 and will either be trivial or contain a large unipotent radical. 相似文献
13.
非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.本文确定了一般广义仿射李代数上所有的Poisson代数结构. 相似文献
14.
R. Holtkamp 《Archiv der Mathematik》2003,80(4):368-383
Several Hopf algebra structures on vector spaces of trees can be found in the literature (cf. [10], [8], [2]). In this paper, we compare the corresponding notions of trees, the multiplications and comultiplications. The Hopf algebras are connected graded or, equivalently, complete Hopf algebras. The Hopf algebra structure on planar binary trees introduced by Loday and Ronco [10] is noncommutative and not cocommutative. We show that this Hopf algebra is isomorphic to the noncommutative version of the Hopf algebra of Connes and Kreimer [3]. We compute its first Lie algebra structure constants in the sense of [7], and show that there is no cogroup structure compatible with the Hopf algebra on planar binary trees. 相似文献
15.
Yuri A. Kordyukov 《Journal of Fixed Point Theory and Applications》2010,7(2):385-399
First, we review the notion of a Poisson structure on a noncommutative algebra due to Block, Getzler and Xu, and we introduce
a notion of a Hamiltonian vector field on a noncommutative Poisson algebra. Then we describe a Poisson structure on a noncommutative
algebra associated with a transversely symplectic foliation and construct a class of Hamiltonian vector fields associated
with this Poisson structure. 相似文献
16.
We present master symmetries of noncommutative differential-difference KP equation by considering Sato approach, where the field variables are defined over associative algebras. The Lie algebraic structures of generalized and master symmetries are given. They form a Virasoro Lie algebraic structure. 相似文献
17.
It is well known that the classical two-dimensional topological field theories are in one-to-one correspondence with the commutative
Frobenius algebras. An important extension of classical two-dimensional topological field theories is provided by open-closed
two-dimensional topological field theories. In this paper we extend open-closed two-dimensional topological field theories
to nonorientable surfaces. We call them Klein topological field theories (KTFT).
We prove that KTFTs bijectively correspond to (in general noncommutative) algebras with certain additional structures, called
structure algebras. The semisimple structure algebras are classified. Starting from an arbitrary finite group, we construct
a structure algebra and prove that it is semisimple.
We define an analog of Hurwitz numbers for real algebraic curves and prove that they are correlators of a KTFT. The structure
algebra of this KTFT is the structure algebra of a symmetric group. 相似文献
18.
Central simple Poisson algebras 总被引:1,自引:0,他引:1
SU Yucai & XU XiaopingDepartment of Mathematics Shanghai Jiaotong University Shanghai China Institute of Mathematics Academy of Mathematics System Sciences Chinese Academy of Sciences Beijing China 《中国科学A辑(英文版)》2004,47(2):245-263
Poisson algebras are fundamental algebraic structures in physics and sym-plectic geometry. However, the structure theory of Poisson algebras has not been well developed. In this paper, we determine the structure of the central simple Poisson algebras related to locally finite derivations, over an algebraically closed field of characteristic zero. The Lie algebra structures of these Poisson algebras are in general not finitely-graded. 相似文献
19.
Zahra BAGHERI 《数学年刊B辑(英文版)》2022,43(2):175-194
Recently, some concepts such as Hom-algebras, Hom-Lie algebras, Hom-Lie admissible algebras, Hom-coalgebras are studied and some classical properties of algebras and some geometric objects are extended on them. In this paper by recalling the concept of Hom-ρ-commutative algebras, the authurs intend to develop some of the most classical results in Riemannian geometry such as metric, connection, torsion tensor, curvature tensor on it and also they discuss about differential operators and get some ... 相似文献
20.
Xiang Tang 《Geometric And Functional Analysis》2006,16(3):731-766
We introduce a new kind of groupoid—a pseudo-étale groupoid, which provides many interesting examples of noncommutative Poisson
algebras as defined by Block, Getzler, and Xu. Following the idea that symplectic and Poisson geometries are the semiclassical
limits of the corresponding quantum geometries, we quantize these noncommutative Poisson algebras in the framework of deformation
quantization.
Received: September 2004 Revision: September 2005 Accepted: September 2005
Dedicated to A. Weinstein on his 60th birthday 相似文献