纠缠代数的导数问题

M. Elhamdadi, A. Makhlouf, S. Silvestrov, E. Zappala
{"title":"纠缠代数的导数问题","authors":"M. Elhamdadi, A. Makhlouf, S. Silvestrov, E. Zappala","doi":"10.1142/s0218196722500424","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.","PeriodicalId":13615,"journal":{"name":"Int. J. Algebra Comput.","volume":"44 1","pages":"985-1007"},"PeriodicalIF":0.0000,"publicationDate":"2022-05-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"Derivation problem for quandle algebras\",\"authors\":\"M. Elhamdadi, A. Makhlouf, S. Silvestrov, E. Zappala\",\"doi\":\"10.1142/s0218196722500424\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.\",\"PeriodicalId\":13615,\"journal\":{\"name\":\"Int. J. Algebra Comput.\",\"volume\":\"44 1\",\"pages\":\"985-1007\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-05-18\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Int. J. Algebra Comput.\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1142/s0218196722500424\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Int. J. Algebra Comput.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1142/s0218196722500424","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 3

摘要

摘要本文的目的是引入并研究纠缠代数的导数概念。更准确地说,我们描述了结构常数上的对称性,为线性映射的导数提供了表征。我们得到了特征为零的二面体四角群的四角代数的导数的完整刻划,并给出了导数的李代数的维数。给出了许多关于零特征和正特征的显式例子和计算。此外,我们研究了非结合结构在Schafer意义上的内推导。我们得到了亚历山大群的群群代数的李变换代数的必要条件,并给出了在低维上的显式计算。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Derivation problem for quandle algebras
The purpose of this paper is to introduce and investigate the notion of derivation for quandle algebras. More precisely, we describe the symmetries on structure constants providing a characterization for a linear map to be a derivation. We obtain a complete characterization of derivations in the case of quandle algebras of dihedral quandles over fields of characteristic zero, and provide the dimensionality of the Lie algebra of derivations. Many explicit examples and computations are given over both zero and positive characteristic. Furthermore, we investigate inner derivations, in the sense of Schafer for non-associative structures. We obtain necessary conditions for the Lie transformation algebra of quandle algebras of Alexander quandles, with explicit computations in low dimensions.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
0
期刊最新文献
Super-biderivations on the planar Galilean conformal superalgebra On the induced partial action of a quotient group and a structure theorem for a partial Galois extension Semigroups locally embeddable into the class of finite semigroups Construction of symmetric cubic surfaces Properties of symbolic powers of edge ideals of weighted oriented graphs
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1