Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-26T04:37:41.545Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected])
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

References

[1]Geck, M., ‘Hecke algebras of finite type are cellular’, Invent. Math. 169 (2007), 501–517.CrossRefGoogle Scholar
[2]Graham, J. J. and Lehrer, G. I., ‘Cellular algebras’, Invent. Math. 123 (1996), 1–34.CrossRefGoogle Scholar
[3]Graham, J. J., Modular Representations of Hecke Algebras and Related Algebras, PhD Thesis, Sydney University, 1995.Google Scholar
[4]Holm, T. and Zimmermann, A., ‘Deformed preprojective algebras of type L: Külshammer spaces and derived equivalences’, J. Algebra 346 (2011), 116–146.CrossRefGoogle Scholar
[5]Koenig, S. and Xi, C. C., ‘A self-injective cellular algebra is weakly symmetric’, J. Algebra 228 (2000), 51–59.CrossRefGoogle Scholar
[6]Li, Y., ‘Centres of symmetric cellular algebras’, Bull. Aust. Math. Soc. 82 (2010), 511–522.CrossRefGoogle Scholar
[7]Xi, C. C., ‘Partition algebras are cellular’, Compositio Math. 119 (1999), 99–109.CrossRefGoogle Scholar
[8]Xi, C. C., ‘On the quasi-heredity of Birman–Wenzl algebras’, Adv. Math. 154 (2000), 280–298.CrossRefGoogle Scholar