论文标题
计算F_2系数的K_2组非交通性组代数
Calculation of a K_2 group of an F_2 coefficients noncommutative group algebra
论文作者
论文摘要
在本文中，计算了一个非共同组的F_2系数组代数（二面体组D_4），分为三个部分：第一部分是引入与代数K理论相关的基础知识，以及MAGURN来计算有限的现场现场系数的方法，以计算有限的现场系数非官能数量的参考[2] 2.在第二部分中，引入了Dennis-Stein符号的操作定律，我们将其与F_2 [D_4]是一个局部环相结合，用于确定K_2（F_2 [D_4]）的直接总和项仅能是Z_2或Z__4。在第三部分中，我们继续利用f_2 [d_4]是本地戒指的事实，并证明了d_1（f_2 [d_4]）组是一个与k_2（f_2 [d_4]）通过操作dennis-stein符号密切相关的亚伯群。 Then, we used group homology and the Kunneth formula of the finite abelian group version to calculate all cases of H_2(D_1(F_2[D_4]),Z) , and substituted the obtained results into the long exact sequence derived from the Hochschild-Serre spectral sequence for testing, and finally constructed the result: K_2(F_2[D_4])=Z_2..
In this paper, the K_2 group of F_2 coefficients group algebra of a noncommutative group with 8 elements(dihedral group D_4 ) is calculated,which is divided into three parts:The first part is the introduction of basic knowledge related to algebra K-theory, and a method of Magurn to calculate finite field coefficients noncommutative finite group algebra in reference [2]. In the second part, operation laws of Dennis-Stein symbols is introduced, and we combined it with the fact that F_2[D_4] is a local ring to determind the direct sum term of K_2(F_2[D_4]) can only be Z_2 or Z_4. In the third part, we continue to make use of the fact that F_2[D_4] is a local ring, and proved that the group D_1(F_2[D_4]) is an abelian group closely related to the group K_2(F_2[D_4]) through operating Dennis-Stein symbols. Then, we used group homology and the Kunneth formula of the finite abelian group version to calculate all cases of H_2(D_1(F_2[D_4]),Z) , and substituted the obtained results into the long exact sequence derived from the Hochschild-Serre spectral sequence for testing, and finally constructed the result: K_2(F_2[D_4])=Z_2..
