论文标题
分级分区代数和Galois扩展
Graded-division algebras and Galois extensions
论文作者
论文摘要
分级分区代数是由G组分级的有限维代数理论中的基础。如果G是Abelian，则可以使用循环结构在中央简单级别的层次级别代数方面对其进行描述。 另一方面，考虑到有限的ABELIAN G组，由于Picco和Platzeck的结果，确定了田野F上的任何中央简单的G级分区代数。 该连接用于根据GALOIS字段扩展L/F与GALOIS组同构为g/k的g/k和k的类别k的类别的k-循环群，以及在l modulo a 2循环的多个群体中，在f中的多态群中，k的2 cocycle具有k/k的类别，将k的g-galois扩展分类。非简单的g-galois扩展是从G的简单T-Galois扩展中诱导的。我们还对有限的G-GradIvision-Division-Division代数进行了分类，并且作为应用，有限的G-Graded细分环。
Graded-division algebras are building blocks in the theory of finite-dimensional associative algebras graded by a group G. If G is abelian, they can be described, using a loop construction, in terms of central simple graded-division algebras. On the other hand, given a finite abelian group G, any central simple G-graded-division algebra over a field F is determined, thanks to a result of Picco and Platzeck, by its class in the (ordinary) Brauer group of F and the isomorphism class of a G-Galois extension of F. This connection is used to classify the simple G-Galois extensions of F in terms of a Galois field extension L/F with Galois group isomorphic to a quotient G/K and the class of a 2-cocycle of K with values in the multiplicative group of L modulo a 2-coboundary with values in the multiplicative group of F, subject to certain conditions. Non-simple G-Galois extensions are induced from simple T-Galois extensions for a subgroup T of G. We also classify finite-dimensional G-graded-division algebras and, as an application, finite G-graded-division rings.
