{"title":"格拉斯曼代数的三元推广","authors":"V. Abramov","doi":"10.3176/phys.math.1996.2/3.05","DOIUrl":null,"url":null,"abstract":"We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula of a change of variables is proved. In analogy with the fermion integral we define an analogue of the Pfaffian for a cubic matrix by means of Gaussian type integral and calculate its explicit form in the case of N = 3.","PeriodicalId":308961,"journal":{"name":"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1996-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"7","resultStr":"{\"title\":\"TERNARY GENERALIZATIONS OF GRASSMANN ALGEBRA\",\"authors\":\"V. Abramov\",\"doi\":\"10.3176/phys.math.1996.2/3.05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula of a change of variables is proved. In analogy with the fermion integral we define an analogue of the Pfaffian for a cubic matrix by means of Gaussian type integral and calculate its explicit form in the case of N = 3.\",\"PeriodicalId\":308961,\"journal\":{\"name\":\"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1996-07-31\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3176/phys.math.1996.2/3.05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Estonian Academy of Sciences. Physics. Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3176/phys.math.1996.2/3.05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We propose the ternary generalization of the classical anti-commutativity and study the algebras whose generators are ternary anti-commutative. The integral over an algebra with an arbitrary number of generators N is defined and the formula of a change of variables is proved. In analogy with the fermion integral we define an analogue of the Pfaffian for a cubic matrix by means of Gaussian type integral and calculate its explicit form in the case of N = 3.
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