{"title":"具有零乘法的有限维津比尔代数的普遍包络代数的自动形态","authors":"D. M. Zhangazinova, A. Naurazbekova","doi":"10.31489/2023m4/173-184","DOIUrl":null,"url":null,"abstract":"In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra U(A) of A. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described.","PeriodicalId":29915,"journal":{"name":"Bulletin of the Karaganda University-Mathematics","volume":" 13","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2023-12-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication\",\"authors\":\"D. M. Zhangazinova, A. Naurazbekova\",\"doi\":\"10.31489/2023m4/173-184\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra U(A) of A. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described.\",\"PeriodicalId\":29915,\"journal\":{\"name\":\"Bulletin of the Karaganda University-Mathematics\",\"volume\":\" 13\",\"pages\":\"\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-12-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin of the Karaganda University-Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31489/2023m4/173-184\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin of the Karaganda University-Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31489/2023m4/173-184","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
近年来，人们对津比尔（对偶莱布尼兹）代数的研究产生了浓厚的兴趣。2010 年，诺拉兹别科娃（A. Naurazbekova）利用格罗布纳-希尔绍夫基的方法，构建了 A 的普遍（乘法）包络代数 U(A) 的基。
Automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication
In recent years there has been a great interest in the study of Zinbiel (dual Leibniz) algebras. Let A be Zinbiel algebra over an arbitrary field K and let e1,e2,...,em,... be a linear basis of A. In 2010 A. Naurazbekova, using the methods of Gro¨bner-Shirshov bases, constructed the basis of the universal (multiplicative) enveloping algebra U(A) of A. Using this result, the automorphisms of the universal enveloping algebra of a finite-dimensional Zinbiel algebra with zero multiplication are described.
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