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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Main Authors: Ming Ding, Zhiqi Chen, Jifu Li
Format: Article
Language:English
Published: AIMS Press 2025-01-01
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.
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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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AT zhiqichen thepropertiesonfmanifoldcoloralgebrasandprefmanifoldcoloralgebras
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AT zhiqichen propertiesonfmanifoldcoloralgebrasandprefmanifoldcoloralgebras
AT jifuli propertiesonfmanifoldcoloralgebrasandprefmanifoldcoloralgebras