共查询到20条相似文献,搜索用时 109 毫秒
1.
Yuly Billig 《代数通讯》2018,46(8):3413-3429
We reprove the results of Jordan [18] and Siebert [30] and show that the Lie algebra of polynomial vector fields on an irreducible a?ne variety X is simple if and only if X is a smooth variety. Given proof is self-contained and does not depend on papers mentioned above. Besides, the structure of the module of polynomial functions on an irreducible smooth a?ne variety over the Lie algebra of vector fields is studied. Examples of Lie algebras of polynomial vector fields on an N-dimensional sphere, non-singular hyperelliptic curves and linear algebraic groups are considered. 相似文献
2.
In this article, we introduce the notion of the equivalence relation, n-isoclinism, between Lie algebras, and obtain some criterions under which Lie algebras are n-isoclinic. In particular, we show that n-isoclinic Lie algebras can be isoclinically embedded into one Lie algebra. Also, we present the notion of an n-stem Lie algebra and prove its existence within an arbitrary n-isoclinism class. In addition, similar to a result of Hekster [6] in the group case, we characterize the n-stem Lie algebras in the n-isoclinism classes which contains at least one finitely generated Lie algebra L with dim (L n+1) finite. 相似文献
3.
In (2009), Towers [10] presented the notion of c-ideality of a subalgebra of a Lie algebra, and gave some characterizations of solvable and supersolvable Lie algebras. In this article, we further investigate the influence of c-ideality of some subalgebras on the structure of Lie algebras. We also obtain some equivalent conditions for supersolvability of a finite dimensional Lie algebra. 相似文献
4.
David J. Winter 《代数通讯》2013,41(4):1093-1126
A Lie algop is a pair (A, L) where A is a commutative algebra and L is a Lie algebra operating on A by derivations. Faithful simple Lie algops (A, L) are of interest because the corresponding Lie algebras AL are simple—with some rare exceptions at characteristic 2. The simplicity and representation theory of Jordan Lie algops is reduced in Winter (2005b) to the simplicity theory of nil Lie algops and the simplicity and representation theory of toral Lie algops. This paper is devoted to building the first of these two theories, the simplicity theory of nil Lie algops, as a structure theory. 相似文献
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Daniel Larsson 《代数通讯》2013,41(12):4303-4318
In this article we apply a method devised in Hartwig, Larsson, and Silvestrov (2006) and Larsson and Silvestrov (2005a) to the simple 3-dimensional Lie algebra 𝔰𝔩2(𝔽). One of the main points of this deformation method is that the deformed algebra comes endowed with a canonical twisted Jacobi identity. We show in the present article that when our deformation scheme is applied to 𝔰𝔩2(𝔽) we can, by choosing parameters suitably, deform 𝔰𝔩2(𝔽) into the Heisenberg Lie algebra and some other 3-dimensional Lie algebras in addition to more exotic types of algebras, this being in stark contrast to the classical deformation schemes where 𝔰𝔩2(𝔽) is rigid. 相似文献
7.
In [9] Giraldo and Merklen studied irreducible morphisms in the categories 𝒞(𝒜) and D?(Λ), where 𝒞(𝒜) is the category of complexes over an abelian Krull–Schmidt category 𝒜 and D?(Λ) is the derived category of the bounded above complexes of finite generate left modules, over an Artin algebra Λ. In this work, we continue the study of irreducible morphism having one finite irreducible truncation. 相似文献
8.
Local Weyl modules were originally defined for affine Lie algebras by Chari and Pressley in [5]. In this paper we extend the notion of local Weyl modules for a Lie algebra 𝔤 ?A, where 𝔤 is any Kac–Moody algebra and A is any finitely generated commutative associative algebra with unit over ?, and prove a tensor product decomposition theorem which generalizes result in [2, 5]. 相似文献
9.
《代数通讯》2013,41(5):2245-2256
Abstract A class of unitary modules is constructed for an extended affine Lie algebra (EALA) co-ordinatized by a quantum torus for |q| = 1 by extending the method developed by Kac and Raina (Kac, V. G., Raina, A. K. (1987). Highest Weight Representations of Infinite Dimensional Lie Algebras. Singapore: World Scientific.) which uses infinite wedge products. By twisting the module by an automorphism (defined by the author Eswara Rao (Eswara Rao, S. (2001). A class of integrable modules for the core of EALA co-ordinated by Quantum Tori. TIFR preprint.) which commutes with anti-linear anti-automorphism, we construct a large class of unitary modules for the EALA. 相似文献
10.
The main result of this article is the explicit calculation of the first cohomology space H 1(𝒦(3), 𝒮Ψ𝒟𝒪(S 1|3)) of the Lie superalgebra 𝒦(3) of contact vector fields on the supercircle S 1|3 with coefficients in the module of superpseudodifferential operators 𝒮Ψ𝒟𝒪(S 1|3). For the supercicles of dimensional 1 | 0, 1 | 1, and 1 | 2, the first cohomology space is computed, respectively, in the following articles: [2, 3, 14]. The case m ≥ 4 is still out of reach, but we give a lower bound for the dimension of the cohomology space and exhibit three nontrivial, 1-cocycles. 相似文献
11.
We study automorphisms of the incidence algebra of a finite quasiordered set M. In particular, we describe explicitly the group of outer automorphisms and give a criterion for any automorphism of this algebra to be a product of an inner one and an automorphism of M, which corrects some results of Spiegel (2001). 相似文献
12.
Fabrizio Zanello 《代数通讯》2013,41(4):1087-1091
The purpose of this note is to supply an upper and a lower bound (which are in general sharp) for the h-vector of a level algebra which is relatively compressed with respect to any arbitrary level algebra A. The useful concept of relatively compressed algebra was recently introduced in Migliore et al. (2005) (whose investigations mainly focused on the particular case of A a complete intersection). The key idea of this note is the simple observation that the level algebras which are relatively compressed with respect to A coincide (after an obvious isomorphism) with the generic level quotients of suitable truncations of A. Therefore, we are able to apply to relatively compressed algebras the main result of our recent work, Zanello (2007). 相似文献
13.
Yang–Baxter operators from algebra structures appeared for the first time in [11, 22, 23]. Later, Yang–Baxter systems from entwining structures were constructed in [8]. In fact, Yang–Baxter systems are equivalent with braid systems. In this paper we show that braidings and entwinings of various algebraic structures—in particular, algebra factorisations—can be constructed from a braid system, whence from a Yang–Baxter system as well. 相似文献
14.
Katharina Kühn 《代数通讯》2013,41(1):75-87
ABSTRACT Baranov and Zhilinskii (1999) have shown a classification theorem for diagonal direct limits of simple Lie algebras. In this work, we will transfer their results to diagonal direct limits of certain matrix groups, and show that homotopy groups are significant invariants for specific classes of direct limit groups. Communicated by B. Allison 相似文献
15.
Iustin Coandă 《代数通讯》2013,41(12):4668-4672
Using the method of Coand? and Trautmann [4], we give a simple proof of a theorem due, in the smooth case, to Tyurin [9]: if a vector bundle E on a c-codimensional locally Cohen–Macaulay closed subscheme X of ? n extends to a vector bundle F on a similar closed subscheme Y of ? N , for every N > n, then E is the restriction to X of a direct sum of line bundles on ? n . Using the same method, we also provide a proof of the Babylonian tower theorem for locally complete intersection subschemes of projective spaces. 相似文献
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Michel Gros 《代数通讯》2013,41(5):2163-2170
Soit p un nombre premier. Nous établissons l'existence de neutralisations de divers complétés de l'algèbre de Weyl quantique spécialisée en une racine de l'unité primitive d'ordre p (qui est “génériquement” une algèbre d'Azumaya) et donnons en particulier un énoncé de neutralisation explicite relevant celui construit en caractéristique p dans [3]. Let p be a prime number. We establish the existence of neutralizations of various completions of the quantum Weyl algebra specialized at a primitive root of unity of prime order p (which is “generically” an Azumaya algebra) and, in particular, we give a statement of explicit neutralization similar to the one built in characteristic p in [3]. 相似文献
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Mamoru Furuya 《代数通讯》2013,41(8):3130-3146
Let A be an analytic algebra over a field k of characteristic p > 0. In this article, for an analytic k-algebra we introduce the concept of analytic pn-basis which generalizes the pn-basis defined in [1], and the concept of an pn-admissible field for an algebraic function field, we give regularity criteria and absolute regularity criteria for an analytic algebra A/k in terms of the higher differential algebra and analytic pn-basis. The results are partial extension of our previous results for affine algebras to the case of analytic algebras (cf. [1, 3]), and these are partial generalization of results of Orbanz in the analytic case (cf. [9]). 相似文献