✦ LIBER ✦

On the Trace of Graded Automorphisms

✍ Scribed by Naihuan Jing; James J Zhang

Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 342 KB
Volume: 189
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.1996.6896

No coin nor oath required. For personal study only.

✦ Synopsis

A be a connected algebra with a graded algebra endomor-

The trace of is defined to be Tr , t s Ý tr ¬ A t . We prove

that Tr , t is a rational function if A is either finitely generated commutative or right noetherian with finite global dimension or regular. A version of Molien's theorem follows in these three cases. If A is 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.

📜 SIMILAR VOLUMES

Gradings, Derivations, and Automorphisms

Gradings, Derivations, and Automorphisms of Nearly Associative Algebras

✍ Jeffrey Bergen; Piotr Grzeszczuk 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 260 KB

In this paper, we examine a class of algebras which includes Lie algebras, Lie color algebras, right alternative algebras, left alternative algebras, antiassociative Ž . algebras, and associative algebras. We call this class of algebras ␣, ␤, ␥ -algebras and we examine gradings of these algebras by

On the Automorphisms of Incidence Algebr

On the Automorphisms of Incidence Algebras

✍ Eugene Spiegel 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 87 KB

Given a locally finite partially ordered set, X, a ring with identity, R, and an automorphism, , of the incidence algebra of X over R, it is determined when is the composite of an inner automorphism, an automorphism of X, and an induced automorphism of R.

On Automorphisms of Subfactors

✍ Phan H. Loi 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 694 KB

We classify, up to outer conjugacy, free actions of Z on an inclusion of hyperfinite type II 1 factors of finite index, of finite depth, and for which the principal graph is one of the following: A n , n 2, E 6 , E 8 , or a finite group. As a consequence, we obtain the classification of hyperfinite

On the Stability of Graded Rings

✍ H.S. Li 📂 Article 📅 1994 🏛 Elsevier Science 🌐 English ⚖ 559 KB

Let \(R=\oplus_{n \in \mathbb{Z}} R_{n}\) be a left Noetherian, left graded regular \(\mathbb{Z}\)-graded ring (i.e., every finitely generated graded \(R\)-module has finite projective dimension). We prove that if every finitely generated graded projective \(R\)-module is graded stably free then eve

On the Variety of Automorphisms of the A

On the Variety of Automorphisms of the Affine Plane

✍ Jean-Philippe Furter 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 273 KB

The main subject of our study is GA , the variety of automophisms of the 2, n affine plane of degree bounded by a positive integer n. After detailing some definitions and notations in Section 1, we give in Section 2 an algorithm to decide whether an endomorphism of the affine plane over an integral

On the Automorphism Group of the One-Roo

On the Automorphism Group of the One-Rooted Binary Tree

✍ A.M. Brunner; Said Sidki 📂 Article 📅 1997 🏛 Elsevier Science 🌐 English ⚖ 339 KB

Let A be the automorphism group of the one-rooted regular binary tree T and 2 G the subgroup of A consisting of those automorphisms admitting a ''finite Ž . description'' in their action on T . Let N G be the normaliser of G in A, let 2 A Ž . Ž . Aut G be the group of automorphisms of G, and let End