共查询到20条相似文献,搜索用时 93 毫秒
1.
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
2.
Samir Bouchiba 《代数通讯》2013,41(7):2431-2445
In this article, we are concerned with the study of the dimension theory of tensor products of algebras over a field k. We introduce and investigate the notion of generalized AF-domain (GAF-domain for short) and prove that any k-algebra A such that the polynomial ring in one variable A[X] is an AF-domain is in fact a GAF-domain, in particular any AF-domain is a GAF-domain. Moreover, we compute the Krull dimension of A? k B for any k-algebra A such that A[X] is an AF-domain and any k-algebra B generalizing the main theorem of Wadsworth in [16]. 相似文献
3.
Thomas Cassidy 《代数通讯》2013,41(9):3742-3752
Vatne [13] and Green and Marcos [9] have independently studied the Koszul-like homological properties of graded algebras that have defining relations in degree 2 and exactly one other degree. We contrast these two approaches, answer two questions posed by Green and Marcos, and find conditions that imply the corresponding Yoneda algebras are generated in the lowest possible degrees. 相似文献
4.
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
5.
《代数通讯》2013,41(4):1011-1022
ABSTRACT The algebras M a, b (E) ? E and M a+b (E) are PI equivalent over a field of characteristic 0 where E is the infinite-dimensional Grassmann algebra. This result is a part of the well-known tensor product theorem. It was first proved by Kemer in 1984–1987 (see Kemer 1991); other proofs of it were given by Regev (1990), and in several particular cases, by Di Vincenzo (1992), and by the authors (2004). Using graded polynomial identities, we obtain a new elementary proof of this fact and show that it fails for the T-ideals of the algebras M 1, 1(E) ? E and M 2(E) when the base field is infinite and of characteristic p > 2. The algebra M a, a (E) ? E satisfies certain graded identities that are not satisfied by M 2a (E). In another paper we proved that the algebras M 1, 1(E) and E ? E are not PI equivalent in positive characteristic, while they do satisfy the same multilinear identities. 相似文献
6.
Adam Hajduk 《代数通讯》2013,41(9):3236-3244
We introduce a concept generalizing classical degenerations of algebras (defined by structure constants) and Crawley-Boevey degenerations introduced in [3]. We prove that if A 0 is such a generalized degeneration of A 1 and the algebras have equal dimensions, then A 0 is a degeneration of A 1 in the classical sense. 相似文献
7.
It is known that the semigroup Sing n of all singular self-maps of X n = {1,2,…, n} has rank n(n ? 1)/2. The idempotent rank, defined as the smallest number of idempotents generating Sing n , has the same value as the rank. (See Gomes and Howie, 1987.) Idempotents generating Sing n can be seen as special cases (with m = r = 2) of (m, r)-path-cycles, as defined in Ay\i k et al. (2005). The object of this article is to show that, for fixed m and r, the (m, r)-rank of Sing n , defined as the smallest number of (m, r)-path-cycles generating Sing n , is once again n(n ? 1)/2. 相似文献
8.
We study absolute valued algebras with involution, as defined in Urbanik (1961). We prove that these algebras are finite-dimensional whenever they satisfy the identity (x, x 2, x) = 0, where (·, ·, ·) means associator. We show that, in dimension different from two, isomorphisms between absolute valued algebras with involution are in fact *-isomorphisms. Finally, we give a classification up to isomorphisms of all finite-dimensional absolute valued algebras with involution. As in the case of a parallel situation considered in Rochdi (2003), the triviality of the group of automorphisms of such an algebra can happen in dimension 8, and is equivalent to the nonexistence of 4-dimensional subalgebras. 相似文献
9.
10.
Paula A. A. B. Carvalho 《代数通讯》2013,41(5):1622-1646
A generalization of down-up algebras was introduced by Cassidy and Shelton (2004), the so-called “generalized down-up algebras”. We describe the automorphism group of conformal Noetherian generalized down-up algebras L(f, r, s, γ) such that r is not a root of unity, listing explicitly the elements of the group. In the last section, we apply these results to Noetherian down-up algebras, thus obtaining a characterization of the automorphism group of Noetherian down-up algebras A(α, β, γ) for which the roots of the polynomial X 2 ? α X ? β are not both roots of unity. 相似文献
11.
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
12.
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
13.
David Nacin 《代数通讯》2018,46(3):1243-1251
The algebras A(Γ), where Γ is a directed layered graph, were first constructed by Gelfand et al. [5]. These algebras are generalizations of the algebras Qn, which are related to factorizations of non-commutative polynomials. It was originally conjectured that these algebras were Koszul. In 2008, Cassidy and Shelton found a counterexample to this claim, a non-Koszul A(Γ) corresponding to a graph Γ with 18 edges and 11 vertices. We produce an example of a directed layered graph Γ with 13 edges and 9 vertices, which produces a non-Koszul A(Γ). We also show this is the minimal example with this property. 相似文献
14.
Let H be a finite-dimensional and semisimple Hopf algebra over an algebraically closed field of characteristic 0 such that H has exactly one isomorphism class of simple modules that have not dimension 1. These Hopf algebras were the object of study in, for instance, [1] and [9]. In this paper we study this property in the context of certain abelian extensions of group algebras and give a group theoretical criterion for such Hopf algebras to be of the above type. We also give a classification result in a special case thereof. 相似文献
15.
Sabine El Khoury 《代数通讯》2013,41(9):3259-3277
In this article, we study height four graded Gorenstein ideals I in k[x, y, z, w] such that I 2 is of height one and generated by three quadrics. After a suitable linear change of variables, I ∩ k[x, y, z] is either Gorenstein or of type two. The former case was studied by Iarrobino and Srinivasan [8] where they give the structure of the ideal and its resolution. We study the latter case and give the structure of these ideals and their minimal resolution. We also explicitly write the form of the generators of I and the maps in the free resolution of R/I. 相似文献
16.
Motivated by the construction of new examples of Artin–Schelter regular algebras of global dimension four, Zhang and Zhang [6] introduced an algebra extension A P [y 1, y 2; σ, δ, τ] of A, which they called a double Ore extension. This construction seems to be similar to that of a two-step iterated Ore extension over A. The aim of this article is to describe those double Ore extensions which can be presented as iterated Ore extensions of the form A[y 1; σ1, δ1][y 2; σ2, δ2]. We also give partial answers to some questions posed in Zhang and Zhang [6]. 相似文献
17.
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
18.
Iwan Praton 《代数通讯》2013,41(3):811-839
Generalized down-up algebras were first introduced in Cassidy and Shelton (2004). Their simple weight modules were classified in Cassidy and Shelton (2004) in the noetherian case, and in Praton (2007) in the non-noetherian case. Here we concentrate on non-noetherian down-up algebras. We show that almost all simple modules are weight modules. We also classify the corresponding primitive ideals. 相似文献
19.
Alexandru Constantinescu 《代数通讯》2013,41(12):4704-4720
The authors in Harima et al. (2003) characterize the Hilbert function of algebras with the Lefschetz property. We extend this characterization to algebras with the Lefschetz property m times. We also give upper bounds for the Betti numbers of Artinian algebras with a given Hilbert function and with the Lefschetz property m times and describe the cases in which these bounds are reached. 相似文献
20.
A. Shabanskaya 《代数通讯》2017,45(6):2633-2661
A sequence of nilpotent Leibniz algebras denoted by Nn,18 is introduced. Here n denotes the dimension of the algebra defined for n≥4; the first term in the sequence is ?18 in the list of four-dimensional nilpotent Leibniz algebras introduced by Albeverio et al. [4]. Then all possible right and left solvable indecomposable extensions over the field ? are constructed so that Nn,18 serves as the nilradical of the corresponding solvable algebras. The construction continues Winternitz’ and colleagues’ program established to classify solvable Lie algebras using special properties rather than trying to extend one dimension at a time. 相似文献