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NAKAYAMA AUTOMORPHISMS OF FROBENIUS CELLULAR ALGEBRAS

Part of: Rings and algebras with additional structure

Published online by Cambridge University Press:  07 June 2012

YANBO LI
YANBO LI*
Affiliation:
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao 066004, PR China (email: liyanbo707@163.com)
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Abstract

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Let A be a finite-dimensional Frobenius cellular algebra with cell datum (Λ,M,C,i). Take a nondegenerate bilinear form f on A. In this paper, we study the relationship among i, f and a certain Nakayama automorphism α. In particular, we prove that the matrix associated with α with respect to the cellular basis is uni-triangular under a certain condition.

Keywords

Frobenius algebrascellular algebrasNakayama automorphisms

MSC classification

Secondary: 16W10: Rings with involution; Lie, Jordan and other nonassociative structures 16W20: Automorphisms and endomorphisms
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 86 , Issue 3 , December 2012 , pp. 515 - 524
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

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