On the Trace of Graded Automorphisms
On the Trace of Graded Automorphisms
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DOI：
10.1006/jabr.1996.6896
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发表时间：
1997-03
影响因子：
0.9
通讯作者：
N. Jing;James J. Zhang
中科院分区：
文献类型：
--
作者：
N. Jing;James J. Zhang
设A = A_d ≥ 0，A_d是具有分次代数自同态σ的连通代数.定义σ的迹为Tr（σ，t）= ∑d ≥ 0 tr（σ|广告）td。本文证明了Tr（σ，t）是有理函数，如果A是全生成交换的或右Noether的有限整体维数的或正则的.在这三种情况下，莫里安定理的一个版本如下。如果A是正则代数或Frobenius代数，我们证明了迹的互易性。我们还部分推广渡边定理的Gorenstein性质的非交换的情况下。
Abstract LetA = ⊕d ≥ 0 Adbe a connected algebra with a graded algebra endomorphism σ. The trace of σ is defined to be Tr(σ, t) = ∑d ≥ 0 tr(σ|Ad)td. We prove that Tr(σ, t) is a rational function ifAis either finitely generated commutative or right noetherian with finite global dimension or regular. A version of Molien's theorem follows in these three cases. IfAis a regular algebra or a Frobenius algebra we prove a reciprocity for the trace. We also partially generalize a theorem of Watanabe on the Gorenstein property to the noncommutative case.