The automorphisms of Petit’s algebras
The automorphisms of Petit’s algebras
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Petit 代数的自同构
DOI：
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发表时间：
2017
期刊：
影响因子：
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通讯作者：
S. Pumplün
中科院分区：
文献类型：
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作者：
C. Brown;S. Pumplün
设σ是域K与固定域F的自同构。本文研究了Petit首先定义的非结合单位代数的自同构，它是结合商代数K[t;σ] scinfK [t;σ]的典范推广，当扭多项式f∈K[t; σ]不变时，得到了非结合单位代数的自同构.如果σ与AutF（K）中的所有自同构可交换且n≥m−1，则计算它们的所有自同构，其中n是σ的阶，m是f的次数，并且当n<m−1时得到部分结果。在KscinF是有限伽罗瓦域扩张的情况下，我们得到了F上这些非结合酉代数的自同构群的结构的更详细的信息。我们也简要地调查时，两个这样的代数是同构的。
ABSTRACT Let σ be an automorphism of a field K with fixed field F. We study the automorphisms of nonassociative unital algebras which are canonical generalizations of the associative quotient algebras K[t;σ]∕fK[t;σ] obtained when the twisted polynomial f∈K[t;σ] is invariant, and were first defined by Petit. We compute all their automorphisms if σ commutes with all automorphisms in AutF(K) and n≥m−1, where n is the order of σ and m the degree of f, and obtain partial results for n<m−1. In the case where K∕F is a finite Galois field extension, we obtain more detailed information on the structure of the automorphism groups of these nonassociative unital algebras over F. We also briefly investigate when two such algebras are isomorphic.