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1.
The paper is a continuation of the authors' study of quasi-hereditary algebras whose Yoneda extension algebras (homological duals) are quasi-hereditary. The so-called standard Koszul quasi-hereditary algebras, presented in this paper, have the property that their extension algebras are always quasi-hereditary. In the natural setting of graded Koszul algebras, the converse also holds: if the extension algebra of a graded Koszul quasi-hereditary algebra is quasi-hereditary, then the algebra must be standard Koszul. This implies that the class of graded standard Koszul quasi-hereditary algebras is closed with respect to homological duality. Another immediate consequence is the fact that all algebras corresponding to the blocks of the category O are standard Koszul.  相似文献   

2.
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L)and central extension H^2(L,F)on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given.  相似文献   

3.
本文继续研究了分段Koszul 代数. 具体地, 给出了一些分段Koszul 代数的判定准则; 作为构造更多分段Koszul 代数例子的尝试, 讨论了分段Koszul 代数的“单点扩张” 和“H-Galois 分次扩张”, 其中H 是有限维的半单余半单Hopf 代数.  相似文献   

4.
郭述锋 《数学学报》2019,62(2):191-200
代数的扩张是指两个代数之间保持单位元的同态映射,设f:B→A是代数的扩张,扩张f的相对整体维数是指所有A-模的相对投射维数的上确界.我们给出了扩张的相对整体维数有限的一个充分必要条件,作为应用,还获得了Hochschild的文[Relative homological algebra, Trans. Am. Math. Soc.,1956,82:246-269]中一个结果的简洁证明.  相似文献   

5.
In this paper, we construct representatives for all equivalence classes of the unital essential extension algebras of Cuntz algebra by the C*-algebras of compact operators on a separable infinite-dimensional Hilbert space. We also compute their K-groups and semigroups and classify these extension algebras up to isomorphism by their semigroups.  相似文献   

6.
In this paper we describe explicitly the generating relations for the Grothendieck groups of trivial extension algebras of tame hereditary algebras.  相似文献   

7.
We consider extension algebras of unital purely infinite simple C*-algebras by purely infinite simple stable C*-algebras. K-theory of such extension algebras is described.  相似文献   

8.
幂零表代数   总被引:1,自引:1,他引:0  
海进科  王志俊 《数学杂志》2007,27(6):641-644
本文研究了幂零表代数的一个有趣的性质,利用表代数的Jordan-Hlder型定理,证明了表代数满足幂零被幂零扩张仍是幂零的,但有限幂零群没有这样的扩张.  相似文献   

9.
文章主要研究n-Lie 代数的扩张问题. 首先利用n-Lie 代数的模作n-Lie 代数的Tθ- 扩张与Tθ*-扩张. 再利用模度量3-Lie 代数,做3-Lie 代数的双扩张. 文章最后利用4- 指标阵构造了m 维3-Lie代数的双扩张.  相似文献   

10.
Recently the space-time foam differential algebras of generalized functions with dense singularities were introduced, motivated by the so called space-time foam structures in General Relativity with dense singularities, and by Quantum Gravity. A variety of applications of these algebras has been presented, among them, a global Cauchy-Kovalevskaia theorem, de Rham cohomology in abstract differential geometry, and so on. So far the space-time foam algebras have only been constructed on Euclidean spaces. In this paper, owing to their relevance in General Relativity among others, the construction of these algebras is extended to arbitrary finite dimensional smooth manifolds. Since these algebras contain the Schwartz distributions, the extension of their construction to manifolds also solves the long outstanding problem of defining distributions on manifolds, and doing so in ways compatible with nonlinear operations. Earlier, similar attempts were made in the literature with respect to the extension of the Colombeau algebras to manifolds, algebras which also contain the distributions. These attempts have encountered significant technical difficulties, owing to the growth condition type limitations the elements of Colombeau algebras have to satisfy near singularities. Since in this paper no any type of such or other growth conditions are required in the construction of space-time foam algebras, their extension to manifolds proceeds in a surprisingly easy and natural way. It is also shown that the space-time foam algebras form a fine and flabby sheaf, properties which are important in securing a considerably large class of singularities which generalized functions can handle.  相似文献   

11.
We discuss certain homological properties of graded algebras whose trivial modules admit nonpure resolutions. Such algebras include both of Artin–Schelter regular algebras of types (12221) and (13431). Under certain conditions, a module with nonpure resolution is decomposed to form an extension by two modules with pure resolutions.  相似文献   

12.
We classify pointed Hopf algebras of dimension 16 over an algebraically closed field of characteristic zero. Apart from the 11 group algebras, there are 29 such Hopf algebras. All of them can be obtained using the Ore extension construction, as described recently by Beattie, the second author, and Grunenfelder.  相似文献   

13.
We give a presentation for the degenerate Ringel-Hall algebras of type B by studying the corresponding generic extension monoid algebras.As an application,it is shown that the degenerate Ringel-Hall algebras of type B admit multiplicative bases.  相似文献   

14.
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the differential graded setting. The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras are discussed.  相似文献   

15.
Shufeng Guo 《代数通讯》2018,46(5):2089-2108
An extension of algebras is a homomorphism of algebras preserving identities. Given an extension f:BA, the relative global dimension of f is defined to be the supremum of relative projective dimensions of all A-modules. In this paper, we compare relative homological dimensions of two extensions of ordinary algebras under certain conditions. As an application, for any natural number n, we present a general method for constructing non-trivial extensions of Artin algebras of relative global dimension at least n.  相似文献   

16.
We extend the notion of monogenic extension to the noncommutative setting, and we study the Hochschild cohomology ring of such an extension. As an application we complete the computation of the cohomology ring of the rank one Hopf algebras begun in [S.M. Burciu, S.J. Witherspoon, Hochschild cohomology of smash products and rank one Hopf algebras, math.RA/0608762, 2006].  相似文献   

17.
Nonassociative quaternion algebras were first discovered over the real numbers independently by Dickson and Albert and provided some of the first examples of nonassociative division algebras. They were later classified completely by Waterhouse. Cyclic algebras can be seen as a natural generalisation of the classical quaternion algebras. With this in mind we generalise nonassociative quaternion algebras and introduce nonassociative cyclic algebras. These provide new examples of nonassociative central division algebras with Nucleus a separable field extension of degree n.  相似文献   

18.
Xiao-Wu Chen 《代数通讯》2013,41(5):1961-1970
We prove that a certain pair of bimodules over two artin algebras gives rise to a triangle equivalence between the singularity categories of the two corresponding trivial extension algebras. Some consequences and an example are given.  相似文献   

19.
W. Turner 《Journal of Algebra》2008,319(10):3975-4007
We study Koszul duality for finite dimensional hereditary algebras, and various generalisations to trivial extension algebras, to Schur algebras, to doubles of Schur bialgebras, and to deformations of doubles of Schur bialgebras. We describe applications to the modular representation theory of symmetric groups.  相似文献   

20.
Necessary and sufficient conditions are found for the possibility of an extension of Invertibility Symbols from a dense subalgebra to its closure. It is proved that such an extension is possible if and only if the closure does not have any Kakutani elements. The extension of Invertibility Symbols from a Banach algebra to the matrix-valued case is also considered. Algebras with Polynomial Identities play an important role here. Applications to algebras generated by two idempotents and to algebras generated by singular integral operators are suggested.  相似文献   

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