共查询到20条相似文献,搜索用时 15 毫秒
1.
Gianfranco Casnati 《代数通讯》2013,41(8):2738-2761
Let k be an algebraically closed field of characteristic 0. We give here a complete classification of local commutative, associative, Artinian, Gorenstein k-algebras with unit, up to multiplicity 9. 相似文献
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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
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Let F be an algebraically closed field and let A and B be arbitrary finite dimensional simple algebras over F. We prove that A and B are isomorphic if and only if they satisfy the same identities. 相似文献
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David J. Winter 《代数通讯》2013,41(11):4153-4169
The classical central simple theory of associative algebras generalizes, in this article, to a central simple theory of nonassociative algebras with operators and a related central irreducible theory of modules. These theories are motivated by, and apply to, problems of constructing and classifying simple Jordan Lie algebras, irreducible modules, and birings. 相似文献
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Alessandro De Stefani 《代数通讯》2013,41(2):729-754
In this article we study Hilbert functions and isomorphism classes of Artinian level local algebras via Macaulay's inverse system. Upper and lower bounds concerning numerical functions admissible for level algebras of fixed type and socle degree are known. For each value in this range we exhibit a level local algebra with that Hilbert function, provided that the socle degree is at most three. Furthermore, we prove that level local algebras of socle degree three and maximal Hilbert function are graded. In the graded case, the extremal strata have been parametrized by Cho and Iarrobino. 相似文献
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J. Z. Gonçalves 《代数通讯》2013,41(8):3113-3121
Let R be a noncommutative central simple algebra, the center k of which is not absolutely algebraic, and consider units a,b of R such that {a,a b } freely generate a free group. It is shown that such b can be chosen from suitable Zariski dense open subsets of R, while the a can be chosen from a set of cardinality |k| (which need not be open). 相似文献
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《代数通讯》2013,41(9):3157-3178
ABSTRACT Pairs (A, L) with A a commutative algebra and L a Lie algebra acting on A by derivations, called Lie algops, are studied as algebraic structures over arbitrary fields of arbitrary characteristic. Lie algops possess modules and tensor products—and are considered with respect to a central simple theory. The simplicity problem of determining the faithful unital simple Lie algops ( A, L ) is of interest since the corresponding Lie algebras AL are usually simple (Jordan, 2000). For locally finite Lie algops, and up to purely inseparable descent, this problem reduces by way of closures to the closed central simplicity problem of determining those which are closed central simple. The simplicity and representation theories for locally nilpotent separably triangulable unital Lie algops are of particular interest because they relate to the problems of classifying simple Lie algebras of Witt type and their representations. Of these, the simplicity theory reduces to that of Jordan Lie algops. The main Theorems 7.3 and 7.4 reduce the simplicity and representation theories for Jordan Lie algops to the simplicity and representation theories for simple nil and toral Lie algops. 相似文献
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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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Simple algebras of Weyl type 总被引:9,自引:0,他引:9
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to
publication 相似文献
14.
Nikolaus Vonessen 《Algebras and Representation Theory》2007,10(5):413-427
Let k be an algebraically closed base field of arbitrary characteristic. In this paper, we study actions of a connected solvable
linear algebraic group G on a central simple algebra Q. The main result is the following: Q can be split G-equivariantly by a finite-dimensional splitting field, provided that G acts “algebraically,” i.e., provided that Q contains a G-stable order on which the action is rational. As an application, it is shown that rational torus actions on prime PI-algebras
are induced by actions on commutative domains.
Presented by Paul Smith. 相似文献
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In this article, we commence to study the real (simple) left-symmetric algebras. From the known classification of certain complex (semi)simple left-symmetric algebras, we classify their corresponding real forms. We not only obtain the classification of real simple left-symmetric algebras in low dimensions, but also find certain examples of real simple left-symmetric algebras in higher dimensions. In particular, there exists a complex simple left-symmetric algebra without any real form. We also give a geometric construction for a class of real simple left-symmetric algebras. At last, we apply the classification results to study some structures related to geometry. 相似文献
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In this paper,some necessary and sufficient conditions that a finite lattice implication algebra is simple are established.Specially,it is proved that a finite lattice implication algebra L is simple if and only if (L,≤) is a chain,if and only if there exists the unique dual atom in L.Also,it is given that a finite lattice implication algebra with order of a prime number is simple. 相似文献
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Enrico Bozzo 《Linear and Multilinear Algebra》1997,42(1):23-41
We introduce the problem of the location of the algebras contained in a matrix space with displacement structure. We present some partial solutions of the problem that unify and generalize various results obtained so far for the spaces of Toeplitz, Loewner and Toeplitz plus Hankel matrices. 相似文献
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We describe the simple special unital Jordan superalgebras with associative even part A whose odd part M is an associative module over A. We prove that each of these superalgebras, not isomorphic to a superalgebra of nondegenerate bilinear superform, is isomorphically embedded into a twisted Jordan superalgebra of vector type. We exhibit a new example of a simple special Jordan superalgebra. We also describe the superalgebras such that M [A,M] 0. 相似文献