共查询到20条相似文献,搜索用时 171 毫秒
1.
CHEN Xiaowu HUANG Hualin & ZHANG Pu Department of Mathematics University of Science Technology of China Hefei China USTC Shanghai Institute for Advanced Studies Shanghai China Mathematical Section the Abdus Salam ICTP Strada Costiera Trieste Italy Department of Mathematics Shanghai Jiao Tong University Shanghai China 《中国科学A辑(英文版)》2006,49(1):9-26
2.
《代数通讯》2013,41(10):5169-5177
Abstract We prove new characterizations of Quasi-co-Frobenius (QcF) coalgebras and co-Frobenius coalgebras. Among them, we prove that a coalgebra is QcF if and only if C generates every left and every right C-comodule. We also prove that every QcF coalgebra is Morita-Takeuchi equivalent to a co-Frobenius coalgebra. 相似文献
3.
I. Paniello 《Linear and Multilinear Algebra》2017,65(5):943-961
We attach two weighted digraphs to any coalgebra C with genetic realization. Algebraically, these digraphs describe the right and left coideal structure of C, whereas genetically they represent the backwards inheritance through the male and female heritage lines, respectively. After establishing the relationship between the strongly connectedness of the attached digraphs and the simplicity of the genetic coalgebras, both digraphs are unified by considering the notion of genetic trigraph. 相似文献
4.
通过将箭图的每个顶点放置一个k-余代数,首先引进了广义路余代数的概念,其次给出了广义路余代数的一些基本性质,还讨论了同构问题.证明了两个正规广义路余代数是同构的当且仅当他们的箭图及对应顶点上的单余代数是同构的.对于满足Codim C_0■1余代数C,证明了对偶Wedderburn-Malcev定理成立.作为广义路余代数的一个应用,推广了点余代数的对偶Gabriel定理. 相似文献
5.
We study classes of relative injective and projective comodules and extend well-known results about projective comodules given
in [7]. The existence of covers and envelopes by these classes of comodules is also studied and used to characterize the projective
dimension of a coalgebra. We also compare this homological coalgebra with the very intensively studied homological algebra
of the dual algebra (see [5]).
This revised version was published online in June 2006 with corrections to the Cover Date. 相似文献
6.
A unique factorization theorem for matroids 总被引:2,自引:0,他引:2
We study the combinatorial, algebraic and geometric properties of the free product operation on matroids. After giving cryptomorphic definitions of free product in terms of independent sets, bases, circuits, closure, flats and rank function, we show that free product, which is a noncommutative operation, is associative and respects matroid duality. The free product of matroids M and N is maximal with respect to the weak order among matroids having M as a submatroid, with complementary contraction equal to N. Any minor of the free product of M and N is a free product of a repeated truncation of the corresponding minor of M with a repeated Higgs lift of the corresponding minor of N. We characterize, in terms of their cyclic flats, matroids that are irreducible with respect to free product, and prove that the factorization of a matroid into a free product of irreducibles is unique up to isomorphism. We use these results to determine, for K a field of characteristic zero, the structure of the minor coalgebra of a family of matroids that is closed under formation of minors and free products: namely, is cofree, cogenerated by the set of irreducible matroids belonging to . 相似文献
7.
On Dual Structures of Novikov-Poisson Algebras 总被引:1,自引:0,他引:1
Jianmiao Cen 《Southeast Asian Bulletin of Mathematics》2001,25(1):7-14
In this paper, the dual structures of Novikov-Poisson algebras will be studied. We will mainly discuss the tenser products of Novikov-Poisson coalgebras and the dual relationships between Novikov-Poisson algebras and Novikov-Poisson coalgebras. The concept of Novikov-Poisson bialgebras is also introduced.AMS Subject Classification (1991)17A30 17D25 17B50 16W30 相似文献
8.
9.
In this paper, we introduce the notion of (*)-serial coalgebras which is a generalization of serial coalgebras. We investigate the properties of (*)-serial coalgebras and their comodules, and obtain sufficient and necessary conditions for a basic coalgebra to be (*)-serial. 相似文献
10.
11.
We consider stability and evolution of complex biological systems, in particular, genetic networks. We focus our attention
on the problem of homeostasis in these systems with respect to fluctuations of an external medium (the problem is posed by
Gromov and Carbone). Using a certain measure of stochastic stability, we show that a generic system with fixed parameters
is unstable, i.e., the probability to support homeostasis converges to zero as the time T goes to infinity. However, if we
consider a population of unstable systems that are capable to evolve (change their parameters), then such a population can
be stable as T → ∞. This means that the probability to survive may be nonzero as T → ∞. Evolution algorithms that provide
stability of populations are not trivial. We show that the mathematical results on evolution algorithms are consistent with
experimental data on genetic evolution. Bibliography: 45 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 325, 2005, pp. 28–60. 相似文献
12.
Stenström introduced the notion of flat object in a locally finitely presented Grothendieck category 𝒜. In this article we investigate this notion in the particular case of the category 𝒜 = C-Comod of left C-comodules, where C is a coalgebra over a field K. Several characterizations of flat left C-comodules are given and coalgebras having enough flat left C-comodules are studied. It is shown how far these coalgebras are from being left semiperfect. As a consequence, we give new characterizations of a left semiperfect coalgebra in terms of flat comodules. Left perfect coalgebras are introduced and characterized in analogy with Bass's Theorem P. Coalgebras whose injective left C-comodules are flat are discussed and related to quasi-coFrobenius coalgebras. 相似文献
13.
V. N. Zhelyabin 《Mathematical Notes》2006,80(3-4):485-490
It is proved that the orthogonal complement to the coradical of a Jordan (alternative) coalgebra coincides with the quasiregular radical of the dual algebra. 相似文献
14.
15.
研究了余代数上余倾斜余模的结构特征,证明了每个余倾斜余模都可以写成不可分解的两两非同构的余模的直和形式,每个余倾斜余模包含所有的内射不可分解模作为直和项.最后构造了余倾斜余模的两个例子. 相似文献
16.
§1. TheEquivalentTheoremoftheCrossedCoproductLetCbealeftH-weaklycomodulecoalgebra[4]withthestructureρ-C(c)=∑c(1)c(2).DbeleftH-modulecoalgebra[2]withthestructure“”.Forα∈Homκ(C,HH)denoteα(c)=∑α1(c)α2(c).Define△-:CD→(CD)(CD)andε-:CD→κasfollow-i… 相似文献
17.
The linear span of isomorphism classes of posets, P, has a Newtonian coalgebra structure. We observe that the ab-index is a Newtonian coalgebra map from the vector space P to the algebra of polynomials in the noncommutative variables a and b. This enables us to obtain explicit formulas showing how the cd-index of the face lattice of a convex polytope changes when taking the pyramid and the prism of the polytope and the corresponding operations on posets. As a corollary, we have new recursion formulas for the cd-index of the Boolean algebra and the cubical lattice. Moreover, these operations also have interpretations for certain classes of permutations, including simsun and signed simsun permutations. We prove an identity for the shelling components of the simplex. Lastly, we show how to compute the ab-index of the Cartesian product of two posets given the ab-indexes of each poset. 相似文献
18.
C. Năstăsescu B. Torrecillas F. Van Oystaeyen 《Algebras and Representation Theory》2008,11(2):179-190
Let C be a coalgebra over a field k. The aim of this paper is to study the following problem : (P) If C is a k-coalgebra such that C is a generator for the category of left comodules, is C a left quasi-co-Frobenius coalgebra ? The converse always holds. We show that if C has a finite coradical series, the answer is positive. 相似文献
19.
In genetic programming (GP), most often the search space grows in a greater than linear fashion as the number of tasks required to be accomplished increases. This is a cause for one of the greatest problems in evolutionary computation; scalability. The aim of the work presented here is to facilitate the evolution of complex designs that have multiple features. We use a combination of mechanisms specifically designed to facilitate the fast evolution of systems with multiple objectives. These mechanisms are; a genetic transposition inspired seeding, a strongly-typed crossover, and a multiobjective optimization. We demonstrate that, when used together, these mechanisms not only improve the performance of GP but also the reliability of the final designs. We investigate the effect of the aforementioned mechanisms, the main focus being on genetic transposition inspired seeding and strongly typed crossover, on the efficiency of GP employed for the coevolution of locomotion gaits and sensing of a simulated snake-like robot (Snakebot). Experimental results show that the mechanism set forth contribute to significant increase in the efficiency of the evolution of fast moving and sensing Snakebots as well as the robustness of the final designs. 相似文献
20.
V. N. Zhelyabin 《Siberian Mathematical Journal》2005,46(6):1050-1061
W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove that a simple infinite-dimensional Jordan superalgebra of vector type possesses a nonzero dual coalgebra. Thereby, we demonstrate that the hypothesis formulated by W. Michaelis for Lie coalgebras fails in the case of Jordan supercoalgebras. 相似文献