共查询到20条相似文献,搜索用时 62 毫秒
1.
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
2.
Victor Petrogradsky 《代数通讯》2017,45(7):2912-2941
The Grigorchuk and Gupta-Sidki groups play fundamental role in modern group theory. They are natural examples of self-similar finitely generated periodic groups. The author constructed their analogue in case of restricted Lie algebras of characteristic 2 [27], Shestakov and Zelmanov extended this construction to an arbitrary positive characteristic [39]. There are a few more examples of self-similar finitely generated restricted Lie algebras with a nil p-mapping, but, as a rule, that algebras have no clear basis and require technical computations. Now we construct a family L(Ξ) of 2-generated restricted Lie algebras of slow polynomial growth with a nil p-mapping, where a field of positive characteristic is arbitrary and Ξ an infinite tuple of positive integers. Namely, GKdimL(Ξ)≤2 for all such algebras. The algebras are constructed in terms of derivations of infinite divided power algebra Ω. We also study their associative hulls A?End(Ω). Algebras L and A are ?2-graded by a multidegree in the generators. If Ξ is periodic then L(Ξ) is self-similar. As a particular case, we construct a continuum subfamily of non-isomorphic nil restricted Lie algebras L(Ξα), α∈?+, with extremely slow growth. Namely, they have Gelfand-Kirillov dimension one but the growth is not linear. For this subfamily, the associative hulls A have Gelfand-Kirillov dimension two but the growth is not quadratic. The virtue of the present examples is that they have clear monomial bases. 相似文献
3.
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
4.
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
5.
Elisabeth Remm 《代数通讯》2017,45(7):2956-2966
The notion of breadth of a nilpotent Lie algebra was introduced and used to approach problems of classification up to isomorphism in [5]. In the present paper, we study this invariant in terms of characteristic sequence, another invariant, introduced by Goze and Ancochea in [1]. This permits to complete the determination of Lie algebras of breadth 2 studied in [5] and to begin the work for Lie algebras with breadth greater than 2. 相似文献
6.
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
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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
9.
John Talboom 《代数通讯》2013,41(4):1795-1808
This article investigates the irreducibility of certain representations for the Lie algebra of divergence zero vector fields on a torus. In [2] Rao constructs modules for the Lie algebra of polynomial vector fields on an N-dimensional torus, and determines the conditions for irreducibility. The current article considers the restriction of these modules to the subalgebra of divergence zero vector fields. It is shown here that Rao's results transfer to similar irreducibility conditions for the Lie algebra of divergence zero vector fields. 相似文献
10.
ABSTRACT We study self-dual coradically graded pointed Hopf algebras with a help of the dual Gabriel theorem for pointed Hopf algebras (van Oystaeyen and Zhang, 2004). The co-Gabriel Quivers of such Hopf algebras are said to be self-dual. An explicit classification of self-dual Hopf quivers is obtained. We also prove that finite dimensional pointed Hopf algebras with self-dual graded versions are generated by group-like and skew-primitive elements as associative algebras. This partially justifies a conjecture of Andruskiewitsch and Schneider (2000) and may help to classify finite dimensional self-dual coradically graded pointed Hopf algebras. 相似文献
11.
In ([11]), we have studied quadratic Leibniz algebras that are Leibniz algebras endowed with symmetric, nondegenerate, and associative (or invariant) bilinear forms. The nonanticommutativity of the Leibniz product gives rise to other types of invariance for a bilinear form defined on a Leibniz algebra: the left invariance, the right invariance. In this article, we study the structure of Leibniz algebras endowed with nondegenerate, symmetric, and left (resp. right) invariant bilinear forms. In particular, the existence of such a bilinear form on a Leibniz algebra 𝔏 gives rise to a new algebra structure ☆ on the underlying vector space 𝔏. In this article, we study this new algebra, and we give information on the structure of this type of algebras by using some extensions introduced in [11]. In particular, we improve the results obtained in [22]. 相似文献
12.
A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra . This determines a depth functor from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows
that the Lie algebras corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras are simple for all i ∈ ω. In particular, the (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras.
Presented by Don Passman. 相似文献
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15.
Katsutoshi Amano 《代数通讯》2013,41(5):1811-1823
In a previous article (Amano and Masuoka, 2005), the author and Masuoka developed a Picard–Vessiot theory for module algebras over a cocommutative pointed smooth Hopf algebra D. By using the notion of Artinian simple (AS)D-module algebras, it generalizes and unifies the standard Picard–Vessiot theories for linear differential and difference equations. The purpose of this article is to define the notion of Liouville extensions of AS D-module algebras and to characterize the corresponding Picard–Vessiot group schemes. 相似文献
16.
Gil Vernik 《代数通讯》2013,41(6):2150-2155
17.
《代数通讯》2013,41(6):3001-3020
Abstract Let L be a positive definite even lattice and let g ∈ Aut L be a fixed point free automorphism of order 3. We determine the twisted Zhu's algebra A ? (V L ) for the lattice vertex operator algebra V L , where ? is an automorphism of V L induced from g. As a result, we show that the set of all irreducible ?-twisted modules for V L (up to isomorphism) are exactly those constructed by Dong and Lepowsky (1996) and Lepowsky (1985). 相似文献
18.
Ahmed Hegazi 《代数通讯》2013,41(12):5237-5256
The paper is devoted to the study of annihilator extensions of Jordan algebras and suggests new approach to classify nilpotent Jordan algebras, which is analogous to the Skjelbred–Sund method for classifying nilpotent Lie algebras [2, 4, 15]. Subsequently, we have classified nilpotent Jordan algebras of dimension up to four. 相似文献
19.
A. Van Daele 《代数通讯》2013,41(6):2235-2249
We extend the Larson–Sweedler theorem to group-cograded multiplier Hopf algebras introduced in Abd El-hafez et al. (2004), by showing that a group-cograded multiplier bialgebra with finite-dimensional unital components is a group-cograded multiplier Hopf algebra if and only if it possesses a nondegenerate left cointegral. We also generalize the theory of multiplier Hopf algebras of discrete type in Van Daele and Zhang (1999) to group-cograded multiplier Hopf algebras. Our results are applicable to Hopf group-coalgebras in the sense of Turaev (2000). Finally, we study regular multiplier Hopf algebras of η -discrete type. 相似文献
20.
Let r ∈ ? be a complex number, and d ∈ ?≥2 a positive integer greater than or equal to 2. Ashihara and Miyamoto [4] introduced a vertex operator algebra V 𝒥 of central charge dr, whose Griess algebra is isomorphic to the simple Jordan algebra of symmetric matrices of size d. In this article, we prove that the vertex operator algebra V 𝒥 is simple if and only if r is not an integer. Further, in the case that r is an integer (i.e., V 𝒥 is not simple), we give a generator system of the maximal proper ideal I r of the VOA V 𝒥 explicitly. 相似文献