{"title":"8次代数上正交对合的上同调不变量","authors":"A. Quéguiner-Mathieu, J. Tignol","doi":"10.1017/IS011006015JKT160","DOIUrl":null,"url":null,"abstract":"Using triality, we define a relative Arason invariant for orthogonal involutions on a -possibly division- central simple algebra of degree 8. This invariant detects hyperbolicity, but it does not detect isomorphism. We produce explicit examples, in index 4 and 8, of nonisomorphic involutions with trivial relative Arason invariant.","PeriodicalId":50167,"journal":{"name":"Journal of K-Theory","volume":"9 1","pages":"333-358"},"PeriodicalIF":0.0000,"publicationDate":"2012-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1017/IS011006015JKT160","citationCount":"8","resultStr":"{\"title\":\"Cohomological invariants for orthogonal involutions on degree 8 algebras\",\"authors\":\"A. Quéguiner-Mathieu, J. Tignol\",\"doi\":\"10.1017/IS011006015JKT160\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Using triality, we define a relative Arason invariant for orthogonal involutions on a -possibly division- central simple algebra of degree 8. This invariant detects hyperbolicity, but it does not detect isomorphism. We produce explicit examples, in index 4 and 8, of nonisomorphic involutions with trivial relative Arason invariant.\",\"PeriodicalId\":50167,\"journal\":{\"name\":\"Journal of K-Theory\",\"volume\":\"9 1\",\"pages\":\"333-358\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2012-04-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1017/IS011006015JKT160\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of K-Theory\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1017/IS011006015JKT160\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of K-Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1017/IS011006015JKT160","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cohomological invariants for orthogonal involutions on degree 8 algebras
Using triality, we define a relative Arason invariant for orthogonal involutions on a -possibly division- central simple algebra of degree 8. This invariant detects hyperbolicity, but it does not detect isomorphism. We produce explicit examples, in index 4 and 8, of nonisomorphic involutions with trivial relative Arason invariant.
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