Hostname: page-component-77c89778f8-m42fx Total loading time: 0 Render date: 2024-07-21T21:55:31.714Z Has data issue: false hasContentIssue false
  • English
  • Français

BONGARTZ τ-COMPLEMENTS OVER SPLIT-BY-NILPOTENT EXTENSIONS

Published online by Cambridge University Press:  30 July 2018

STEPHEN ZITO
STEPHEN ZITO*
Affiliation:
Mathematics Faculty, University of Connecticut-Waterbury, Waterbury, CT 06702USA e-mail: stephen.zito@uconn.edu
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 C be a finite dimensional algebra with B a split extension by a nilpotent bimodule E, and let M be a τC-rigid module with U its Bongartz τC-complement. If the induced module, M ⊗CB, is τB-rigid, we give a necessary and sufficient condition for U ⊗CB to be its Bongartz τB-complement. If M is τB-rigid, we again provide a necessary and sufficient condition for U ⊗CB to be its Bongartz τB-complement.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 2 , May 2019 , pp. 461 - 470
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

REFERENCES

1. Adachi, T., Iyama, O. and Reiten, I., τ-tilting theory, Compos. Math. 150 (3) (2014), 415–452.Google Scholar
2. Assem, I. and Marmaridis, N., Tilting modules over split-by-nilpotent extensions, Comm. Algebra 26 (1998), 1547–1555.Google Scholar
3. Assem, I., Simson, D. and Skowronski, A., Elements of the representation theory of associative algebras, 1: Techniques of representation theory, London Mathematical Society Student Texts 65 (Cambridge University Press, 2006).Google Scholar
4. Assem, I. and Zacharia, D., Full embeddings of almost split sequences over split-by-nilpotent extensions, Coll. Math. 81 (1) (1999), 21–31.Google Scholar
5. Auslander, M. and Smalø, S. O., Almost split sequences in subcategories, J. Algebra 69 (2) (1981), 426–454.Google Scholar
6. Schiffler, R. and Serhiyenko, K., Induced and coinduced modules in cluster-tilted algebras, J. Algebra 472 (2017), 226–258.Google Scholar