共查询到20条相似文献,搜索用时 15 毫秒
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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
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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
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In this paper, based on the results in [8] we give a monomial basis for q-Schur superalgebra and then a presentation for it. The presentation is different from that in [12]. Imitating [3] and [7], we define the infinitesimal and the little q-Schur superalgebras. We give a “weight idempotent presentation” for infinitesimal q-Schur superalgebras. The BLM bases and monomial bases of little q-Schur superalgebras are obtained, and dimension formulas of infinitesimal and little q-Schur superalgebras are deduced. 相似文献
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In this article, we compute the first space of cohomology of Vect (? n|n ), the Lie superalgebra of vector fields on the supermanifold ? n|n with coefficients in 𝒻 (? n|n ), the space of smooth functions on ? n|n . We give a super analog of the cohomologies of vector fields that where studied for instance by Fuchs [2]. This work allows us to classify the deformations of the action of Vect(? n|n ) on 𝒻 (? n|n ). 相似文献
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Naihong Hu 《代数通讯》2013,41(9):3202-3220
This article is the sequel to [11] to study the deformed structures and representations of two-parameter quantum groups U r, s (𝔤) associated to the finite dimensional simple Lie algebras 𝔤. An equivalence of the braided tensor categories 𝒪 r, s and 𝒪 q under the assumption rs ?1 = q 2 is explicitly established. 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
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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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Evgeny Chibrikov 《代数通讯》2013,41(11):4014-4035
Sabinin algebras are algebraic objects that capture the local structure of analytic loops in the same way in which Lie algebras capture the local structure of Lie groups. They were introduced by Sabinin and Mibeev [13]. In 1962, Shirshov [20] suggested a scheme for choosing bases of a free Lie algebra that generalizes the Hall and Lyndon–Shirshov bases. In this article, we generalize the Shirshov scheme for the case of Sabinin algebras. 相似文献
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Matthew F. Ragland 《代数通讯》2013,41(10):3242-3252
A group G is called a Hall𝒳-group if G possesses a nilpotent normal subgroup N such that G/N′ is an 𝒳-group. A group G is called an 𝒳o-group if G/Φ(G) is an 𝒳-group. The aim of this article is to study finite solvable Hall𝒳-groups and 𝒳o-groups for the classes of groups 𝒯, 𝒫𝒯, and 𝒫𝒮𝒯. Here 𝒯, 𝒫𝒯, and 𝒫𝒮𝒯 denote, respectively, the classes of groups in which normality, permutability, and Sylow-permutability are transitive relations. Finite solvable 𝒯-groups, 𝒫𝒯-groups, and 𝒫𝒮𝒯-groups were globally characterized, respectively, in Gaschütz (1957), Zacher (1964), and Agrawal (1975). Here we arrive at similar characterizations for finite solvable Hall𝒳-groups and 𝒳o-groups where 𝒳 ∈ {𝒯, 𝒫𝒯, 𝒫𝒮𝒯}. A key result aiding in the characterization of these groups is their possession of a nilpotent residual which is a nilpotent Hall subgroup of odd order. The main result arrived at is Hall𝒫𝒮𝒯 = 𝒯o for finite solvable groups. 相似文献
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Stacy L. Beun 《代数通讯》2013,41(4):1334-1352
Symmetric k-varieties are a generalization of symmetric spaces to general fields. Orbits of a minimal parabolic k-subgroup acting on a symmetric k-variety are essential in the study of symmetric k-varieties and their representations. In this article, we present the classification of these orbits for the group SL(2,k) for a number of base fields k, including finite fields and the 𝔭-adic numbers. We use the characterization in Helminck and Wang (1993), which requires one to first classify the orbits of the θ-stable maximal k-split tori under the action of the k-points of the fixed point group. 相似文献
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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