The properties on F-manifold color algebras and pre-F-manifold color algebras
The concept of F-manifold algebras is an algebraic expression of F-manifolds. In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra. We develop the representation theory of an F-manifold color algebra and sho...
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| Language: | English |
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AIMS Press
2025-01-01
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| Series: | Electronic Research Archive |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/era.2025005 |
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| author | Ming Ding Zhiqi Chen Jifu Li |
| author_facet | Ming Ding Zhiqi Chen Jifu Li |
| author_sort | Ming Ding |
| collection | DOAJ |
| description | The concept of F-manifold algebras is an algebraic expression of F-manifolds. In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra. We develop the representation theory of an F-manifold color algebra and show that F-manifold color algebras admitting non-degenerate symmetric bilinear forms are coherence F-manifold color algebras. The concept of pre-F-manifold color algebras is also presented, and using this definition one can construct F-manifold color algebras. These results extend some properties of F-manifold algebras. |
| format | Article |
| id | doaj-art-22d980109b764d1c85451b7e7dd0b902 |
| institution | OA Journals |
| issn | 2688-1594 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Electronic Research Archive |
| spelling | doaj-art-22d980109b764d1c85451b7e7dd0b9022025-08-20T01:54:41ZengAIMS PressElectronic Research Archive2688-15942025-01-013318710110.3934/era.2025005The properties on F-manifold color algebras and pre-F-manifold color algebrasMing Ding0Zhiqi Chen1Jifu Li2School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, ChinaSchool of Mathematics and Statistics, Guangdong University of Technology, Guangzhou 510520, ChinaSchool of Science, Tianjin University of Technology, Tianjin 300384, ChinaThe concept of F-manifold algebras is an algebraic expression of F-manifolds. In this paper, we provide the definition of an F-manifold color algebra, which can be viewed as a natural generalization of an F-manifold algebra. We develop the representation theory of an F-manifold color algebra and show that F-manifold color algebras admitting non-degenerate symmetric bilinear forms are coherence F-manifold color algebras. The concept of pre-F-manifold color algebras is also presented, and using this definition one can construct F-manifold color algebras. These results extend some properties of F-manifold algebras.https://www.aimspress.com/article/doi/10.3934/era.2025005lie color algebraf-manifold algebraf-manifold color algebrarepresentation theorypre-f-manifold color algebra |
| spellingShingle | Ming Ding Zhiqi Chen Jifu Li The properties on F-manifold color algebras and pre-F-manifold color algebras Electronic Research Archive lie color algebra f-manifold algebra f-manifold color algebra representation theory pre-f-manifold color algebra |
| title | The properties on F-manifold color algebras and pre-F-manifold color algebras |
| title_full | The properties on F-manifold color algebras and pre-F-manifold color algebras |
| title_fullStr | The properties on F-manifold color algebras and pre-F-manifold color algebras |
| title_full_unstemmed | The properties on F-manifold color algebras and pre-F-manifold color algebras |
| title_short | The properties on F-manifold color algebras and pre-F-manifold color algebras |
| title_sort | properties on f manifold color algebras and pre f manifold color algebras |
| topic | lie color algebra f-manifold algebra f-manifold color algebra representation theory pre-f-manifold color algebra |
| url | https://www.aimspress.com/article/doi/10.3934/era.2025005 |
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