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NAKAYAMA AUTOMORPHISMS OF FROBENIUS CELLULAR ALGEBRAS

  • YANBO LI (a1)

Abstract

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.

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References

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[1]Geck, M., ‘Hecke algebras of finite type are cellular’, Invent. Math. 169 (2007), 501517.
[2]Graham, J. J. and Lehrer, G. I., ‘Cellular algebras’, Invent. Math. 123 (1996), 134.
[3]Graham, J. J., Modular Representations of Hecke Algebras and Related Algebras, PhD Thesis, Sydney University, 1995.
[4]Holm, T. and Zimmermann, A., ‘Deformed preprojective algebras of type L: Külshammer spaces and derived equivalences’, J. Algebra 346 (2011), 116146.
[5]Koenig, S. and Xi, C. C., ‘A self-injective cellular algebra is weakly symmetric’, J. Algebra 228 (2000), 5159.
[6]Li, Y., ‘Centres of symmetric cellular algebras’, Bull. Aust. Math. Soc. 82 (2010), 511522.
[7]Xi, C. C., ‘Partition algebras are cellular’, Compositio Math. 119 (1999), 99109.
[8]Xi, C. C., ‘On the quasi-heredity of Birman–Wenzl algebras’, Adv. Math. 154 (2000), 280298.
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NAKAYAMA AUTOMORPHISMS OF FROBENIUS CELLULAR ALGEBRAS

  • YANBO LI (a1)

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