On the determination of the Singer transfer
Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] with the degree of each generator xi being 1, where F2 denote the prime field of two elements, and let GLk be the general linear group over F2 which acts regularly on Pk. We study the algebraic transfer constructed by Singer [1] usin...
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| Format: | Article |
| Language: | English |
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Vietnam Ministry of Science and Technology
2018-03-01
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| Series: | Vietnam Journal of Science, Technology and Engineering |
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| Online Access: | https://vietnamscience.vjst.vn/index.php/vjste/article/view/250 |
| _version_ | 1797937762301640704 |
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| author | Sum Nguyen |
| author_facet | Sum Nguyen |
| author_sort | Sum Nguyen |
| collection | DOAJ |
| description |
Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] with the degree of each generator xi being 1, where F2 denote the prime field of two elements, and let GLk be the general linear group over F2 which acts regularly on Pk.
We study the algebraic transfer constructed by Singer [1] using the technique of the Peterson hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra A, TorA k,k+d(F2, F2), to the subspace of F2⊗APk consisting of all the GLk-invariant classes of degree d.
In this paper, by using the results on the Peterson hit problem we present the proof of the fact that the Singer algebraic transfer is an isomorphism for k 3. This result has been proved by Singer in [1] for k 2 and by Boardman in [2] for k = 3. We show that the fourth Singer transfer is also an isomorphism in certain internal degrees. This result is new and it is different from the ones of Bruner, Ha and Hung [3], Chon and Ha [4], Ha [5], Hung and Quynh [6], Nam [7].
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| first_indexed | 2024-04-10T18:49:22Z |
| format | Article |
| id | doaj.art-862fe34259d84c53b611d672e61b5e80 |
| institution | Directory Open Access Journal |
| issn | 2525-2461 2615-9937 |
| language | English |
| last_indexed | 2024-04-10T18:49:22Z |
| publishDate | 2018-03-01 |
| publisher | Vietnam Ministry of Science and Technology |
| record_format | Article |
| series | Vietnam Journal of Science, Technology and Engineering |
| spelling | doaj.art-862fe34259d84c53b611d672e61b5e802023-02-01T08:20:47ZengVietnam Ministry of Science and TechnologyVietnam Journal of Science, Technology and Engineering2525-24612615-99372018-03-0160110.31276/VJSTE.60(1).03On the determination of the Singer transferSum Nguyen0Department of Mathematics, Quy Nhon University, Vietnam Let Pk be the graded polynomial algebra F2[x1, x2, . . . , xk] with the degree of each generator xi being 1, where F2 denote the prime field of two elements, and let GLk be the general linear group over F2 which acts regularly on Pk. We study the algebraic transfer constructed by Singer [1] using the technique of the Peterson hit problem. This transfer is a homomorphism from the homology of the mod-2 Steenrod algebra A, TorA k,k+d(F2, F2), to the subspace of F2⊗APk consisting of all the GLk-invariant classes of degree d. In this paper, by using the results on the Peterson hit problem we present the proof of the fact that the Singer algebraic transfer is an isomorphism for k 3. This result has been proved by Singer in [1] for k 2 and by Boardman in [2] for k = 3. We show that the fourth Singer transfer is also an isomorphism in certain internal degrees. This result is new and it is different from the ones of Bruner, Ha and Hung [3], Chon and Ha [4], Ha [5], Hung and Quynh [6], Nam [7]. https://vietnamscience.vjst.vn/index.php/vjste/article/view/250algebraic transferpolynomial algebrasteenrod algebra |
| spellingShingle | Sum Nguyen On the determination of the Singer transfer Vietnam Journal of Science, Technology and Engineering algebraic transfer polynomial algebra steenrod algebra |
| title | On the determination of the Singer transfer |
| title_full | On the determination of the Singer transfer |
| title_fullStr | On the determination of the Singer transfer |
| title_full_unstemmed | On the determination of the Singer transfer |
| title_short | On the determination of the Singer transfer |
| title_sort | on the determination of the singer transfer |
| topic | algebraic transfer polynomial algebra steenrod algebra |
| url | https://vietnamscience.vjst.vn/index.php/vjste/article/view/250 |
| work_keys_str_mv | AT sumnguyen onthedeterminationofthesingertransfer |