Continuous quivers of type A (I) Foundations
- Author
- Kiyoshi Igusa, Daisie Rock (UGent) and Gordana Todorov
- Organization
- Abstract
- We generalize quivers of type A to continuous quivers of type A and prove initial results about pointwise finite-dimensional representations. Among these results is the classification of those representations and a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pointwise finite-dimensional projective representations. Finally, we prove that many of the properties of finite-dimensional representations of quivers of type A_n also hold for finitely generated representations of continuous quivers of type A. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other cluster structures of type A.
- Keywords
- General Mathematics, Representation theory, Continuous quivers, Representations of quivers
Citation
Please use this url to cite or link to this publication: http://hdl.handle.net/1854/LU-8748232
- MLA
- Igusa, Kiyoshi, et al. “Continuous Quivers of Type A (I) Foundations.” RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, vol. 72, 2023, pp. 833–68, doi:10.1007/s12215-021-00691-x.
- APA
- Igusa, K., Rock, D., & Todorov, G. (2023). Continuous quivers of type A (I) Foundations. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 72, 833–868. https://doi.org/10.1007/s12215-021-00691-x
- Chicago author-date
- Igusa, Kiyoshi, Daisie Rock, and Gordana Todorov. 2023. “Continuous Quivers of Type A (I) Foundations.” RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO 72: 833–68. https://doi.org/10.1007/s12215-021-00691-x.
- Chicago author-date (all authors)
- Igusa, Kiyoshi, Daisie Rock, and Gordana Todorov. 2023. “Continuous Quivers of Type A (I) Foundations.” RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO 72: 833–868. doi:10.1007/s12215-021-00691-x.
- Vancouver
- 1.Igusa K, Rock D, Todorov G. Continuous quivers of type A (I) Foundations. RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. 2023;72:833–68.
- IEEE
- [1]K. Igusa, D. Rock, and G. Todorov, “Continuous quivers of type A (I) Foundations,” RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, vol. 72, pp. 833–868, 2023.
@article{8748232,
abstract = {{We generalize quivers of type A to continuous quivers of type A and prove initial results about pointwise finite-dimensional representations. Among these results is the classification of those representations and a decomposition theorem, recovering results of Botnan and Crawley-Boevey. We also classify the indecomposable pointwise finite-dimensional projective representations. Finally, we prove that many of the properties of finite-dimensional representations of quivers of type A_n also hold for finitely generated representations of continuous quivers of type A. This is the self-contained foundational part of a series of works to study a generalization of continuous clusters categories and their relationship to other cluster structures of type A.}},
author = {{Igusa, Kiyoshi and Rock, Daisie and Todorov, Gordana}},
issn = {{0009-725X}},
journal = {{RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO}},
keywords = {{General Mathematics,Representation theory,Continuous quivers,Representations of quivers}},
language = {{eng}},
pages = {{833--868}},
title = {{Continuous quivers of type A (I) Foundations}},
url = {{http://doi.org/10.1007/s12215-021-00691-x}},
volume = {{72}},
year = {{2023}},
}
- Altmetric
- View in Altmetric