论文标题
Quandle的共同体学，扩展和自动形态学
Quandle cohomology, extensions and automorphisms
论文作者
论文摘要
该论文建立了共同学，扩展和Quandles的自动形态之间的新关系。我们得出了一个四个项的精确序列，该序列与Quandle 1 cocycles，第二次Quandle的同胞和某些Abelian Quandles延伸的自动形态。还建立了涉及动力学共同体类别的该序列的非亚伯式对应物，并给出了一些提升Quandle自动形态学的应用。将一个组的核心和广义的亚历山大·夸尔（Alexander Quandle）视为群体的伴奏，从群众类别到组类别，我们证明这些函子将群体的扩展映射到集团的扩展。最后，我们构建了一些自然组的同态，从一个组的第二个共同体到其核心和共轭量的第二个共同体。
The paper establishes new relationship between cohomology, extensions and automorphisms of quandles. We derive a four term exact sequence relating quandle 1-cocycles, second quandle cohomology and certain group of automorphisms of an abelian extension of quandles. A non-abelian counterpart of this sequence involving dynamical cohomology classes is also established, and some applications to lifting of quandle automorphisms are given. Viewing the construction of the conjugation, the core and the generalised Alexander quandle of a group as an adjoint functor of some appropriate functor from the category of quandles to the category of groups, we prove that these functors map extensions of groups to extensions of quandles. Finally, we construct some natural group homomorphisms from the second cohomology of a group to the second cohomology of its core and conjugation quandles.
