{"title":"联立和乔丹烈无穷级数","authors":"S. V. Pchelintsev","doi":"10.1007/s10469-024-09755-0","DOIUrl":null,"url":null,"abstract":"<p>We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index 2n + 1 if and only if its algebra of multiplications is Lie nilpotent of index 2n. Finally, we prove a product theorem for Jordan algebras.</p>","PeriodicalId":7422,"journal":{"name":"Algebra and Logic","volume":null,"pages":null},"PeriodicalIF":0.4000,"publicationDate":"2024-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Associative and Jordan Lie Nilpotent Algebras\",\"authors\":\"S. V. Pchelintsev\",\"doi\":\"10.1007/s10469-024-09755-0\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index 2n + 1 if and only if its algebra of multiplications is Lie nilpotent of index 2n. Finally, we prove a product theorem for Jordan algebras.</p>\",\"PeriodicalId\":7422,\"journal\":{\"name\":\"Algebra and Logic\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2024-09-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Algebra and Logic\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s10469-024-09755-0\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"LOGIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Algebra and Logic","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10469-024-09755-0","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"LOGIC","Score":null,"Total":0}
We look at the interconnection between Lie nilpotent Jordan algebras and Lie nilpotent associative algebras. It is proved that a special Jordan algebra is Lie nilpotent if and only if its associative enveloping algebra is Lie nilpotent. Also it turns out that a Jordan algebra is Lie nilpotent of index 2n + 1 if and only if its algebra of multiplications is Lie nilpotent of index 2n. Finally, we prove a product theorem for Jordan algebras.
期刊介绍：
This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions.
Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences.
All articles are peer-reviewed.
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