共查询到20条相似文献,搜索用时 46 毫秒
1.
We show that the symplectic groups PSp6(q) are Hurwitz for all q = p m ≥ 5, with p an odd prime. The result cannot be improved since, for q even and q = 3, it is known that PSp6(q) is not Hurwitz. In particular, n = 6 turns out to be the smallest degree for which a family of classical simple groups of degree n, over 𝔽 p m , contains Hurwitz groups for infinitely many values of m. This fact, for a given (possibly large) p, also follows from [9] and [10]. 相似文献
2.
Zhixiang Wu 《代数通讯》2013,41(9):3869-3897
In the present article, we introduce G-graded left symmetric H-pseudoalgebras, where G is a grading group, and H is a cocommutative Hopf algebra. Some results about associative H-pseudoalgebras in [23] are generalized. The commutator algebras of the G-graded left symmetric H-pseudo-algebras are Lie H-pseudoalgebras, which are classified when the grading group is trivial in [3]. We investigate the left symmetric structure of Lie H-pseudoalgebras W(𝔟), S(𝔟), and He defined in [3]. 相似文献
3.
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
4.
Juan C. Gutierrez Fernandez Claudia I. Garcia José Ignacio Martinez M. L. R. Montoya 《代数通讯》2013,41(10):4481-4497
Whether or not a finite-dimensional, commutative, power-associative nilalgebra is solvable is a well-known open problem. In this paper, we describe commutative, power-associative nilalgebras of dimension n ≥ 6 and nilindex n ? 1 based on the condition that n ? 4 ≤ dim 𝔄3 ≤ n ? 3. This paper is a continuation of [10], where we describe commutative power-associative nilalgebras of dimension and nilindex n. We observe that the Jordan case was obtained by L. Elgueta and A. Suazo in [2]. 相似文献
5.
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
6.
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
7.
José Antonio Cuenca Mira 《代数通讯》2013,41(12):4057-4067
A well-known Ingelstam's Theorem asserts that every real Hilbert space A with an associative unital product satisfying ‖ xy‖ ≤ ‖ x‖ ‖ y‖ and ‖ 1‖ = 1 is isomorphic to the reals ?, or the complex numbers ?, or the quaternions ?. This note deals with a nonunital and nonassociative extension of the Ingelstam Theorem. So the assumptions about associativity and existence of unity are weakened to the existence of a nonzero central idempotent e such that ‖ ex‖ = ‖e‖ ‖ x‖ for all x, and that in A holds a determined kind of algebraic identity strictly weaker that alternativeness. We prove that, up to isomorphisms, there are only seven algebras satisfying these assumptions, even without the requirement of completeness. On the other hand, Section 3 presents another characterization of the obtained algebras with the flavor of one of the main theorems in Bhatt et al. (1998). 相似文献
8.
9.
This article is a sequel of [4], where we defined supervaluations on a commutative semiring R and studied a dominance relation ? ≥ ψ between supervaluations ? and ψ on R, aiming at an enrichment of the algebraic tool box for use in tropical geometry. A supervaluation ?: R → U is a multiplicative map from R to a supertropical semiring U, cf. [4], [7], [8], [5], [9], with further properties, which mean that ? is a sort of refinement, or covering, of an m-valuation (= monoid valuation) v: R → M. In the most important case, that R is a ring, m-valuations constitute a mild generalization of valuations in the sense of Bourbaki [1], while ? ≥ ψ means that ψ: R → V is a sort of coarsening of the supervaluation ?. If ?(R) generates the semiring U, then ? ≥ ψ iff there exists a “transmission” α: U → V with ψ = α ○ ?. Transmissions are multiplicative maps with further properties, cf. [4, Section 5]. Every semiring homomorphism α: U → V is a transmission, but there are others which lack additivity, and this causes a major difficulty. In the main body of the article we study surjective transmissions via equivalence relations on supertropical semirings. We put special emphasis on homomorphic equivalence relations. Even those are often much more complicated than congruences by ideals in usual commutative algebra. 相似文献
10.
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
11.
Yunchuan Yin 《代数通讯》2013,41(2):547-565
ABSTRACT The “W-graph” concept was introduced by Kazhdan and Lusztig in their influential article Kazhdan and Lusztig (1979). If W is a Coxeter group, then a W-graph provides a method for constructing a matrix representation of the Hecke algebra ? associated with W (the degree of the representation being the number of vertices of the W-graph). The aim of this note is to explicitly construct all the irreducible representations of ? when W is of type D 4 and D 5. 相似文献
12.
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
13.
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
14.
Let Fq be a finite field with q elements, n ≥ 2 a positive integer, and T(n, q) the semigroup of all n × n upper triangular matrices over Fq. The rank-decreasing graph 𝕋 of T(n, q) is a directed graph which has T(n, q) as vertex set, and there is a directed edge from A ∈ T(n, q) to B ∈ T(n, q) if and only if r(AB) < r(B). The zero-divisor graph 𝒯 of T(n, q), with vertex set of all nonzero zero-divisors of T(n, q) and there is a directed edge from a vertex A to a vertex B if and only if AB = 0, can be viewed as a subgraph of 𝕋. In [16], L. Wang has determined the automorphisms of the zero-divisor graph 𝒯 of T(n, q). In this article, by applying the main result of [17] we determine the automorphisms of the rank-decreasing graph 𝕋 of T(n, q). 相似文献
15.
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
16.
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
17.
Let Λ be an Artin algebra over a commutative Artinian ring, k. If M is a finitely generated left Λ -module, we denote by Ω (M) the kernel of η M : P M → M a minimal projective cover. We prove that if M and N are finitely generated left Λ -modules and Ext Λ 1 (M, M) = 0, Ext Λ 1 (N, N) = 0, then M? N if and only if M/rad M? N/rad N and Ω (M)? Ω (N). Now if k is an algebraically closed field and (d i ) i?? is a sequence of nonnegative integers almost all of them zero, then we prove that the family of objects X ? b (Λ), the bounded derived category of Λ, with Hom b (Λ)(X,X[1]) = 0 and dim k H i (X) = d i for all i ? ?, has only a finite number of isomorphism classes (see Huisgen-Zimmermann and Saorín, 2001). 相似文献
18.
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
19.