排序方式: 共有17条查询结果,搜索用时 234 毫秒
1.
We study domain theoretic properties of complexity spaces. Although the so-called complexity space is not a domain for the usual pointwise order, we show that, however, each pointed complexity space is an ω-continuous domain for which the complexity quasi-metric induces the Scott topology, and the supremum metric induces the Lawson topology. Hence, each pointed complexity space is both a quantifiable domain in the sense of M. Schellekens and a quantitative domain in the sense of P. Waszkiewicz, via the partial metric induced by the complexity quasi-metric. 相似文献
2.
The quantum doubles of a certain class of rank two pointed Hopf algebras are considered. The socle of the tensor product of two such modules is computed, and formulas similar to the ones in [4] are obtained. Cases when such a tensor product is completely irreducible are also given in the last section. 相似文献
3.
Anton Dochtermann 《Journal of Combinatorial Theory, Series A》2009,116(1):180-194
The notion of ×-homotopy from [Anton Dochtermann, Hom complexes and homotopy theory in the category of graphs, European J. Combin., in press] is investigated in the context of the category of pointed graphs. The main result is a long exact sequence that relates the higher homotopy groups of the space Hom∗(G,H) with the homotopy groups of Hom∗(G,HI). Here Hom∗(G,H) is a space which parameterizes pointed graph maps from G to H (a pointed version of the usual Hom complex), and HI is the graph of based paths in H. As a corollary it is shown that πi(Hom∗(G,H))≅×[G,ΩiH], where ΩH is the graph of based closed paths in H and ×[G,K] is the set of ×-homotopy classes of pointed graph maps from G to K. This is similar in spirit to the results of [Eric Babson, Hélène Barcelo, Mark de Longueville, Reinhard Laubenbacher, Homotopy theory of graphs, J. Algebraic Combin. 24 (1) (2006) 31-44], where the authors seek a space whose homotopy groups encode a similarly defined homotopy theory for graphs. The categorical connections to those constructions are discussed. 相似文献
4.
In Rips complexes and covers in the uniform category (Brodskiy et al. [4]) we define, following James (1990) [9], covering maps of uniform spaces and introduce, inspired by Berestovskii and Plaut (2007) [2], the concept of generalized uniform covering maps. In this paper we investigate when these covering maps are induced by group actions which allows us to relate our covering maps to those in Berestovskii and Plaut (2007) [2]. Also, as an application of our results we present an exposition of Prajs' (2002) [16] homogeneous curve that is path-connected but not locally connected. 相似文献
5.
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
6.
Paul Gilmartin 《代数通讯》2019,47(7):2833-2842
Let k be a field and let H denote a pointed Hopf k-algebra with antipode S. We are interested in determining the order of S. Building on the work done by Taft and Wilson in [7], we define an invariant for H, denoted mH, and prove that the value of this invariant is connected to the order of S. In the case where char k?=?0, it is shown that if S has finite order then it is either the identity or has order 2?mH. If in addition H is assumed to be coradically graded, it is shown that the order of S is finite if and only if mH is finite. We also consider the case where char k?=?p?>?0, generalizing the results of [7] to the infinite-dimensional setting. 相似文献
7.
Fernando Fantino 《代数通讯》2013,41(10):4426-4434
8.
We clarify the relationship between ideals, clots, and normal subobjects in a pointed regular category with finite coproducts.
Partially supported by South African NRF
Research partially supported by the Hungarian National Foundation for Scientific Research grant no. K61007. 相似文献
9.
Iván Ezequiel Angiono 《Advances in Mathematics》2010,225(6):3545-3575
Let m be a positive integer, not divisible by 2, 3, 5, 7. We generalize the classification of basic quasi-Hopf algebras over cyclic groups of prime order given in Etingof and Gelaki (2006) [11] to the case of cyclic groups of order m. To this end, we introduce a family of non-semisimple radically graded quasi-Hopf algebras A(H,s), constructed as subalgebras of Hopf algebras twisted by a quasi-Hopf twist, which are not twist equivalent to Hopf algebras. Any basic quasi-Hopf algebra over a cyclic group of order m is either semisimple, or is twist equivalent to a Hopf algebra or a quasi-Hopf algebra of type A(H,s). 相似文献
10.
M. Cuntz 《Journal of Combinatorial Theory, Series A》2011,118(4):1350-1363
We extend the classification of finite Weyl groupoids of rank two. Then we generalize these Weyl groupoids to ‘reflection groupoids’ by admitting non-integral entries of the Cartan matrices. This leads to the unexpected observation that the spectrum of the cluster algebra of type An−3 completely describes the set of finite reflection groupoids of rank two with 2n objects. 相似文献