论文标题
相关代数的良好成绩和自动形态群体
Fine gradings and automorphism groups on associative algebras
论文作者
论文摘要
首先，我们证明，在分级简化的Unital联合代数的稳定器中，其分级组是Abelian的任何内部自动形态，都是同质元素的结合。现在，考虑一个阿贝尔集团对联想代数的分级，以使代数是简单的，并在分级的左左理想中满足DCC。我们提供了必要和足够的条件，以使分级良好。然后，我们假设满足了这些必要条件之一，并且我们计算分级的自动形态群体。结果是根据分级分区代数的自动形态组表示的。最后，我们计算了渐变划分代数的自动形态基团在地下磁场为实数的情况下，而基础代数（忽略分级）很简单且尺寸有限。
First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an associative algebra such that the algebra is graded-simple and satisfies the DCC on graded left ideals. We give necessary and sufficient conditions for the grading to be fine. Then we assume that one of these necessary conditions to be fine is satisfied, and we compute the automorphism groups of the grading; the results are expressed in terms of the automorphism groups of a graded-division algebra. Finally we compute the automorphism groups of graded-division algebras in the case in which the ground field is the field of real numbers, and the underlying algebra (disregarding the grading) is simple and of finite dimension.
