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On the representation dimension and finitistic dimension of special multiserial algebras


Author: Sibylle Schroll
Journal: Proc. Amer. Math. Soc. 147 (2019), 2275-2280
MSC (2010): Primary 16G10, 05E10
DOI: https://doi.org/10.1090/proc/14230
Published electronically: March 1, 2019
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Abstract: For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of monomial and self-injective special multiserial algebras is less than or equal to three. This implies that the finitistic dimension conjecture holds for all special multiserial algebras.


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Sibylle Schroll
Affiliation: Department of Mathematics, University of Leicester, University Road, Leicester LE1 7RH, United Kingdom
Email: schroll@leicester.ac.uk

DOI: https://doi.org/10.1090/proc/14230
Keywords: Representation dimension, radical embedding, splitting daturm, special multiserial algebra
Received by editor(s): July 26, 2017
Received by editor(s) in revised form: November 9, 2017, and January 24, 2018
Published electronically: March 1, 2019
Additional Notes: Part of this work took place during a visit of the author to the University of São Paulo. The author would like to thank Eduardo Marcos for his hospitality. This work was supported through the EPSRC fellowship grant EP/P016294/1.
Dedicated: Dedicated to Ed Green on the occasion of his $70$th birthday
Communicated by: Jerzy Weyman
Article copyright: © Copyright 2019 American Mathematical Society