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Self-injective Cellular Algebras Whose Representation Type are Tame of Polynomial Growth

A Publisher Correction to this article was published on 04 May 2019

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Abstract

We classify Morita equivalence classes of indecomposable self-injective cellular algebras which have polynomial growth representation type, assuming that the characteristic of the base field is different from two. This assumption on the characteristic is for the cellularity to be a Morita invariant property.

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  • 04 May 2019

    The original version of this article unfortunately contains mistakes introduced during the production phase.

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Acknowledgments

The first author is supported by the JSPS Grant-in-Aid for Scientific Research 15K04782 and the last author is supported by the JSPS Grant-in-Aid for Scientific Research 16K17565.

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Correspondence to R. Kase.

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The ​original ​version ​of ​this ​article ​was ​revised. The mistakes are on the incorrect cross-referencing of Theorem 6.8, Theorem 7.1, Theorem 7.16, Theorem 7.20, Proposition 5.4, Proposition 5.5, Proposition 6.2, Proposition 6.4, Proposition 6.5, Proposition 6.6, Proposition 6.7, Proposition 7.2, Proposition 7.4, Proposition 7.7, Proposition 7.9, Proposition 7.12, Proposition 7.14, Proposition 7.19, Lemma 5.3, Lemma 6.3, Lemma 7.6, Lemma 7.17, Lemma 7.18, Definition 7.3, Definition 7.5, Definition 7.8, Definition 7.10, Definition 7.13, Definition 7.15 found in sections 1, 5, 6, 7, 8. This is due to the change in the numbering of subsections 5.1, 6.1, 6.2, 6.3, 6.4, 7.1, 7.2, 7.3, and 7.4.

Presented by: Steffen Koenig

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Ariki, S., Kase, R., Miyamoto, K. et al. Self-injective Cellular Algebras Whose Representation Type are Tame of Polynomial Growth. Algebr Represent Theor 23, 833–871 (2020). https://doi.org/10.1007/s10468-019-09872-w

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Keywords

  • Self-injective algebra
  • Cellular algebra
  • Domestic type
  • Polynomial growth