Algebraic Morse theory via Homological Perturbation Lemma
Fuente:
arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866918097763434496 |
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| author | Chen, Jun Liu, Yuming Zhou, Guodong |
| author_facet | Chen, Jun Liu, Yuming Zhou, Guodong |
| contents | As a generalization of the classical killing-contractible-complexes lemma, we present algebraic Morse theory via homological perturbation lemma, in a form more general than existing presentations in the literature. Two-sided Anick resolutions due to E.~Sköldberg are generalised to algebras given by quivers with relations and a minimality criterion is provided as well. Two applications of algebraic Morse theory are presented. It is shown that the Chinese algebra of rank $n\geq 1$ is homologically smooth and of global dimension $\frac{n(n+1)}{2}$, and the minimal two-sided projective resolution of a Koszul algebra is constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_10165 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Algebraic Morse theory via Homological Perturbation Lemma Chen, Jun Liu, Yuming Zhou, Guodong K-Theory and Homology Rings and Algebras 18G35, 16E05, 16E10 As a generalization of the classical killing-contractible-complexes lemma, we present algebraic Morse theory via homological perturbation lemma, in a form more general than existing presentations in the literature. Two-sided Anick resolutions due to E.~Sköldberg are generalised to algebras given by quivers with relations and a minimality criterion is provided as well. Two applications of algebraic Morse theory are presented. It is shown that the Chinese algebra of rank $n\geq 1$ is homologically smooth and of global dimension $\frac{n(n+1)}{2}$, and the minimal two-sided projective resolution of a Koszul algebra is constructed. |
| title | Algebraic Morse theory via Homological Perturbation Lemma |
| topic | K-Theory and Homology Rings and Algebras 18G35, 16E05, 16E10 |
| url | https://arxiv.org/abs/2404.10165 |