共查询到19条相似文献,搜索用时 140 毫秒
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N-半单代数与蕴涵代数 总被引:8,自引:4,他引:4
研究了有限结合代数与各种蕴涵代数的联系,得到了一些有趣的结果:N-半单代数的中心幂等元集G(R)按照“→”或者“*”等运算分别构成与蕴涵代数(F I代数、BCK代-数、BC I代-数、BCC代-数、W a jsberg代数等)等价的代数系统。 相似文献
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粗糙集代数与MV代数 总被引:2,自引:0,他引:2
讨论粗糙集代数与MV代数的关系以及由粗糙集代数构造MV代数的方法.粗糙集代数本身具有格结构,证明了在适当选取蕴涵及乘积运算之后,粗糙集代数就成为MV代数. 相似文献
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范中平 《高校应用数学学报(A辑)》2016,(2):225-232
通过从余代数的角度构造Hop玳数的块系统,给出了非余半单余代数和纯非余半单余代数具有容许性的必要条件.其应用简化了45维和105维Hop玳数的分类,为有限维Hopf代数的分类提供了新的方法. 相似文献
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在一类无限维非交换Hopf代数上,借助其Hopf理想,构造出商Hopf代数,讨论了此商代数上的有限维不可约模,得出此非平凡不可约模的维数一定是2. 相似文献
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In this paper, we study (associative) Nijenhuis algebras, with emphasis on the relationship between the category of Nijenhuis algebras and the categories of NS algebras and related algebras. This is in analogy to the well-known theory of the adjoint functor from the category of Lie algebras to that of associative algebras, and the more recent results on the adjoint functor from the categories of dendriform and tridendriform algebras to that of Rota-Baxter algebras. We first give an explicit construction of free Nijenhuis algebras and then apply it to obtain the universal enveloping Nijenhuis algebra of an NS algebra. We further apply the construction to determine the binary quadratic nonsymmetric algebra, called the N-dendriform algebra, that is compatible with the Nijenhuis algebra. As it turns out, the N-dendriform algebra has more relations than the NS algebra. 相似文献
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We provide an introduction to the theory of interior-point algorithms of optimization based on the theory of Euclidean Jordan algebras. A short-step path-following algorithm for the convex quadratic problem on the domain, obtained as the intersection of a symmetric cone with an affine subspace, is considered. Connections with the Linear monotone complementarity problem are discussed. Complexity estimates in terms of the rank of the corresponding Jordan algebra are obtained. Necessary results from the theory of Euclidean Jordan algebras are presented. 相似文献
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非交换的Poisson代数同时具有(未必交换的)结合代数和李代数两种代数结构,且结合代数和李代数之间满足所谓的Leibniz法则.本文确定了一般广义仿射李代数上所有的Poisson代数结构. 相似文献
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Ualbai Umirbaev 《代数通讯》2017,45(7):2809-2820
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric algebras of derivations are studied. Simple left-symmetric algebras of derivations and Novikov algebras of derivations are described. It is also proved that the positive part of the left-symmetric algebra of derivations of a free nonassociative symmetric m-ary algebra in one free variable is generated by one derivation and some right nilpotent derivations are described. 相似文献
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Carlos J. Gutiérrez Fernández 《代数通讯》2013,41(2):653-667
In the present paper we give new properties on the Peirce decomposition for principal train algebras and we study for first time the Peirce decomposition for plenary train algebras. Next, we show interesting and important open problems for train algebras. In particular, an old problem for genetic algebras is solved. Thus, we prove that every genetic algebra is plenary train algebra. 相似文献
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Mohamed Boucetta 《代数通讯》2013,41(10):4185-4195
A flat Lorentzian Lie algebra is a left symmetric algebra endowed with a symmetric bilinear form of signature (?, +,…, +) such that left multiplications are skew-symmetric. In geometrical terms, a flat Lorentzian Lie algebra is the Lie algebra of a Lie group with a left-invariant Lorentzian metric with vanishing curvature. In this article, we show that any flat nonunimodular Lorentzian Lie algebras can be obtained as a double extension of flat Riemannian Lie algebras. As an application, we give all flat nonunimodular Lorentzian Lie algebras up to dimension 4. 相似文献
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Askar Dzhumadil’daev 《代数通讯》2018,46(1):129-142
We prove that assosymmetric algebras under the Jordan product are Lie triple algebras. A Lie triple algebra is called special if it is isomorphic to a subalgebra of the plus-algebra of some assosymmetric algebra. We establish that the Glennie identity of degree 8 is valid for special Lie triple algebras, but not for all Lie triple algebras. 相似文献
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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
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The relationships between piecewise-Koszul algebras and other “Koszul-type” algebras are discussed. The Yoneda-Ext algebra
and the dual algebra of a piecewise-Koszul algebra are studied, and a sufficient condition for the dual algebra A
! to be piecewise-Koszul is given. Finally, by studying the trivial extension algebras of the path algebras of Dynkin quivers
in bipartite orientation, we give explicit constructions for piecewise-Koszul algebras with arbitrary “period” and piecewise-Koszul
algebras with arbitrary “jump-degree”. 相似文献