共查询到20条相似文献,搜索用时 15 毫秒
1.
Andrew Dolphin 《代数通讯》2013,41(12):5141-5158
In this article, we present a decomposition theorem for unitary spaces over a central simple division algebra with involution in characteristic 2. This is a generalization of a decomposition result for quadratic forms in characteristic 2 from [4] and extends a generalization of the Witt decomposition theorem for nonsingular spaces in this setting to cover spaces that may be singular. 相似文献
2.
We define a notion of Morita equivalence between algebras with antiautomorphisms such that two equivalent algebras have the same category of sesquilinear forms. This generalizes the Morita equivalence of algebras with involutions defined by Fröhlich and Mc Evett [5], and their categories of ?-hermitian forms. For two Morita equivalent algebras with involution, with an additional technical property (which is true for central simple algebras), we define a new algebra with antiautomorphism, called the orthogonal sum, which generalizes the usual notion of orthogonal sum of forms. We explore the invariants of this sum. 相似文献
3.
In [7] we introduced the notion of full quivers of representations of algebras, which are more explicit than quivers of algebras, and better suited for algebras over finite fields. Here, we consider full quivers as a combinatorial tool in order to describe PI-varieties of algebras. We apply the theory to clarify the proofs of diverse topics in the literature: Determining which relatively free algebras are weakly Noetherian, determining when relatively free algebras are finitely presented, presenting a quick proof for the rationality of the Hilbert series of a relatively free PI-algebra, and explaining counterexamples to Specht's conjecture for varieties of Lie algebras. 相似文献
4.
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
5.
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
6.
Álvaro Muñoz 《代数通讯》2018,46(9):3873-3888
In this paper we give a complete classification of pointed fusion categories over ? of global dimension 8. We first classify the equivalence classes of pointed fusion categories of dimension 8, and then we proceed to determine which of these equivalence classes have equivalent categories of modules following the procedure presented in [9, 11]. The results of this paper permit to recover the classification of twisted quantum doubles of groups of order 8 up to gauge equivalence of braided quasi-Hopf algebras that was previously done in [6] and [5]. 相似文献
7.
It is unknown whether a power series ring over a strongly clean ring is, itself, always strongly clean. Although a number of authors have shown that the above statement is true in certain special cases, the problem remains open, in general. In this article, we look at a class of strongly clean rings, which we call the optimally clean rings, over which power series are strongly clean. This condition is motivated by work in [10] and [11]. We explore the properties of optimally clean rings and provide many examples, highlighting the role that this new class of rings plays in investigating the question of strongly clean power series. 相似文献
8.
Jean-Yves Chemin 《偏微分方程通讯》2015,40(5):878-896
By applying Wiegner's method in [16], we first prove the large time decay estimate for the global solutions of a 2.5 dimensional Navier-Stokes system, which is a sort of singular perturbed 2-D Navier-Stokes system in three space dimension. As an application of this decay estimate, we give a simplified proof for the global wellposedness result in [6] for 3-D Navier-Stokes system with one slow variable. Let us also mention that compared with the assumptions for the initial data in [6], here the assumptions in Theorem 1.3 are weaker. 相似文献
9.
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
10.
11.
Héctor Suárez 《代数通讯》2017,45(10):4569-4580
Pre-Koszul and Koszul algebras were defined by Priddy [15]. There exist some relations between these algebras and the skew PBW extensions defined in [8]. In [24] we gave conditions to guarantee that skew PBW extensions over fields it turns out homogeneous pre-Koszul or Koszul algebra. In this paper we complement these results defining graded skew PBW extensions and showing that if R is a finite presented Koszul 𝕂-algebra then every graded skew PBW extension of R is Koszul. 相似文献
12.
Frank Koster 《Numerical Functional Analysis & Optimization》2013,34(7-8):802-819
Because of the implementation of numerical solution algorithms for the nonstationary Navier–Stokes equations of an incompressible fluid on massively parallel computers iterative methods are of special interest. A red–black pressure–velocity iteration that allows an efficient parallelization based on a domain decomposition [3] will be analyzed in this paper. We prove the equivalence of the pressure–velocity iteration (PUI) by Chorin/Hirt/Cook [1, 2] with a SOR iteration to solve a Poisson equation for the pressure. We show this on a 2D rectangle with some special outflow boundary conditions and Dirichlet data for the velocity elsewhere. This equivalence allows us to prove the convergence of that iteration scheme. We also discuss the stability of the occurring discrete Laplacian in discrete Sobolev spaces. 相似文献
13.
The results of [7] and [2] gave a recursive construction for all quasi-hereditary and standardly stratified algebras starting with local algebras and suitable bimodules. Using the notion of stratifying pairs of subcategories, introduced in [3], we generalize these earlier results to construct recursively all CPS-stratified algebras. 相似文献
14.
William O’Donovan 《代数通讯》2017,45(3):1314-1322
We establish upper and lower bounds on the dimension of the space spanned by the symmetric powers of the natural character of generalized symmetric groups. We adapt the methods of Savitt and Stanley from [4] to obtain bounds both over the complex numbers and in prime characteristic. 相似文献
15.
In this article we use new regularity and stability estimates for Alexandrov solutions to Monge-Ampère equations, recently established by De Philippis and Figalli [14], to provide global in time existence of distributional solutions to the semigeostrophic equations on the 2-dimensional torus, under very mild assumptions on the initial data. A link with Lagrangian solutions is also discussed. 相似文献
16.
GRADINGS OF SIMPLE JORDAN ALGEBRAS AND THEIR RELATION TO THE GRADINGS OF SIMPLE ASSOCIATIVE ALGEBRAS
《代数通讯》2013,41(9):4095-4102
In this paper we describe all group gradings of the simple Jordan algebra of a non-degenerate symmetric form on a vector space over a field of characteristic different from 2. If we use the notion of the Clifford algebra, then we are able to recover some of the gradings on matrix algebras obtained in an entirely different way in [BSZ]. 相似文献
17.
We extend in several directions a complete convergence theorem for row sums from an array of rowwise independent random variables obtained by Sung, Volodin, and Hu [8] to an array of rowwise independent random elements taking values in a real separable Rademacher type p Banach space. An example is presented which illustrates that our result extends the Sung, Volodin, and Hu result even for the random variable case. 相似文献
18.
Chao Zhang 《代数通讯》2013,41(8):3509-3517
We define the global cohomological range for artin algebras, and define the derived bounded algebras to be the algebras with finite global cohomological range, then we prove the first Brauer–Thrall type theorem for bounded derived categories of artin algebras, i.e., derived bounded algebras are precisely the derived finite algebras. Moreover, the main theorem establishes that the derived bounded artin algebras are just piecewise hereditary algebras of Dynkin type, and can be also characterized as those artin algebras with derived dimension zero, which can be regarded as a generalization of the results of Han–Zhang [11, Theorem 1] and Chen–Ye–Zhang [4, Theorem] in the context of finite-dimensional algebras over algebraically closed fields, respectively. 相似文献
19.
We consider the Ginzburg-Landau functional defined over a bounded and smooth three dimensional domain. Supposing that the magnetic field is comparable with the second critical field and that the Ginzburg-Landau parameter is large, we determine a precise asymptotic formula for the minimizing energy. In particular, this shows how bulk superconductivity decreases in average as the applied magnetic field approaches the second critical field from below. Other estimates are also obtained which allow us to obtain, in a subsequent paper [19], a fine characterization of the second critical field. The approach relies on a careful analysis of several limiting energies, which is of independent interest. 相似文献
20.
Ryutaroh Matsumoto 《代数通讯》2013,41(1):401-405
In Hai and Thin [1], there is a theorem, stating that every locally nilpotent subnormal subgroup in a division ring D is central (see [1, Theoerem 2.2]). Unfortunately, there is some mistake in the proof of this theorem. In this note, we give the another proof of this theorem. 相似文献