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81.
《Indagationes Mathematicae》2017,28(1):145-169
A matchbox manifold with one-dimensional leaves which has equicontinuous holonomy dynamics must be a homogeneous space, and so must be homeomorphic to a classical Vietoris solenoid. In this work, we consider the problem, what can be said about a matchbox manifold with equicontinuous holonomy dynamics, and all of whose leaves have at most polynomial growth type? We show that such a space must have a finite covering for which the global holonomy group of its foliation is nilpotent. As a consequence, we show that if the growth type of the leaves is polynomial of degree at most 3, then there exists a finite covering which is homogeneous. If the growth type of the leaves is polynomial of degree at least 4, then there are additional obstructions to homogeneity, which arise from the structure of nilpotent groups. 相似文献
82.
Dean Crnković B.G. Rodrigues Sanja Rukavina Vladimir D. Tonchev 《Discrete Mathematics》2017,340(10):2472-2478
This paper completes the enumeration of quasi-symmetric 2- designs supported by the dual code of the binary linear code spanned by the lines of , initiated in Rodrigues and Tonchev (2015). It is shown that supports exactly 30,264 nonisomorphic quasi-symmetric 2- designs. The automorphism groups of the related strongly regular graphs are computed. 相似文献
83.
《Mathematische Nachrichten》2017,290(14-15):2341-2355
In this paper, we use the powerful tool Milnor bases to determine all the locally symmetric left invariant Riemannian metrics up to automorphism, on 3‐dimensional connected and simply connected Lie groups, by solving system of polynomial equations of constants structure of each Lie algebra . Moreover, we show that E 0(2) is the only 3‐dimensional Lie group with locally symmetric left invariant Riemannian metrics which are not symmetric. 相似文献
84.
Seidon Alsaody 《代数通讯》2017,45(6):2401-2416
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form n over a field k of characteristic not two, and a category arising from an action of the projective similarity group of n on certain pairs of automorphisms of the group scheme PGO+(n) defined over k. This extends results recently obtained in the same direction for symmetric composition algebras. We also derive known results on composition algebras from our equivalence. 相似文献
85.
Automorphic loops, or A-loops, are loops in which all inner mappings are automorphisms. We investigated A-loops arising from a Lie algebra and describe their automorphism group. Also, we identify and describe their inner mapping group. 相似文献
86.
William O’Donovan 《代数通讯》2017,45(3):1314-1322
87.
Anatolii V. Zhuchok 《代数通讯》2017,45(4):1639-1656
Loday introduced the notion of a dimonoid and constructed the free dimonoid. The paper concerns the variety theory of dimonoids. We recall and summarize the results obtained by Loday, the author as well as others on the structure of some relatively free dimonoids. This part of the paper should be viewed as a survey, however we include some new ideas in the last sections. Namely, we construct a free (?z;rs)-dimonoid, a free (rs;rz)-dimonoid, a free rs-dimonoid, a free (rb;rs)-dimonoid, a free (rs;rb)-dimonoid and characterize the least (?z;rs)-congruence, the least (rs;rz)-congruence, the least rs-congruence, the least (rb;rs)-congruence and the least (rs;rb)-congruence on the free dimonoid. We also establish that the automorphism groups of constructed free algebras are isomorphic to the symmetric group and the semigroups of the free rs-dimonoid are anti-isomorphic. 相似文献
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