{"title":"A double construction of quadratic anticenter-symmetric Jacobi-Jordan algebras","authors":"Essossolim Cyrille Haliya, Gbevewou Damien Houndedji","doi":"10.56415/qrs.v31.03","DOIUrl":null,"url":null,"abstract":"This work addresses some relevant characteristics and properties of anticenter-symmetric Jacobi-Jordan algebras such as bimodules, matched pairs. Besides, the Jacobi-Jordan admissible algebra is defined; a special emphasis is given to a double construction of quadratic anticenter-symmetric algebras. We then follow this theory with the main properties and related algebraic structures of an anticenter-symmetric JJ algebra, namely the anti-Zinbiel algebras. Finally, we discuss the double construction of some classes of the two dimensional anticenter-symmetric JJ algebras.","PeriodicalId":38681,"journal":{"name":"Quasigroups and Related Systems","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2023-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Quasigroups and Related Systems","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.56415/qrs.v31.03","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
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Abstract
This work addresses some relevant characteristics and properties of anticenter-symmetric Jacobi-Jordan algebras such as bimodules, matched pairs. Besides, the Jacobi-Jordan admissible algebra is defined; a special emphasis is given to a double construction of quadratic anticenter-symmetric algebras. We then follow this theory with the main properties and related algebraic structures of an anticenter-symmetric JJ algebra, namely the anti-Zinbiel algebras. Finally, we discuss the double construction of some classes of the two dimensional anticenter-symmetric JJ algebras.
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