Transfert algébrique et action du groupe linéaire sur les puissances divisées modulo 2

Nam, Tran

doi:10.5802/aif.2399

Cited by 53 publications

(97 citation statements)

References 23 publications

(40 reference statements)

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“…By applying this technique for k = 4, 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]. In those works it is shown only that the fourth Singer transfer detects certain families of elements in Ext 4, * A (F 2 , F 2 ), and fails to detect others.…”

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confidence: 38%

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On the determination of the Singer transfer

Sum¹

2018

VJSTE

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Abstract:Let P k be the graded polynomial algebra F 2 [x 1 , x 2 , . . . , x k ] with the degree of each generator x i being 1, where F2 denote the prime field of two elements, and let GL k be the general linear group over F 2 which acts regularly on P k .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, Tor

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confidence: 38%

“…It is a useful tool in describing the homology groups of the Steenrod algebra, Tor A k,k+d (F 2 , F 2 ). This transfer was studied by Boardman [2], Bruner, Ha and Hung [3], Ha [5], Hung [9], Chon and Ha [4,10,11], Minami [12], Nam [7], Hung and Quynh [6], the present author [13] and others.…”

Section: Introductionmentioning

confidence: 99%

On the determination of the Singer transfer

Sum¹

2018

VJSTE

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“…(See Boardman [1], Bruner, Hà and Hưng [2], Carlisle and Wood [3], Crabb and Hubbuck [4], Giambalvo and Peterson [5], Hà [6], Hưng [7], Hưng and Nam [8,9], Hưng and Peterson [10,11], Janfada and Wood [12,13], Kameko [14,15], Minami [17], Mothebe [18,19], Nam [20,21], Repka and Selick [25], Silverman [26], Silverman and Singer [27], Singer [29], Walker and Wood [35,36,37], Wood [39,40] and others. )…”

Section: Introduction and Statement Of Resultsmentioning

confidence: 99%

“…Suppose there is a linear relation 3 4 } is the set of all the admissible monomials for A-module P 4 in degree 21.…”

Section: Sqmentioning

confidence: 99%

On the Peterson hit problem

Sum¹

2015

Advances in Mathematics

487

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Abstract. We study the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra P k := F 2 [x 1 , x 2 , . . . , x k ] as a module over the mod-2 Steenrod algebra, A. In this paper, we study a minimal set of generators for A-module P k in some so-called generic degrees and apply these results to explicitly determine the hit problem for k = 4. Dedicated to Prof. N. H. V. Hưng on the occasion of his sixtieth birthday Introduction and statement of resultsLet V k be an elementary abelian 2-group of rank k. Denote by BV k the classifying space of V k . It may be thought of as the product of k copies of the real projective space RP ∞ . ThenHere the cohomology is taken with coefficients in the prime field F 2 of two elements.Being the cohomology of a space, P k is a module over the mod-2 Steenrod algebra A. The action of A on P k is explicitly given by the formulaand subject to the Cartan formulafor f, g ∈ P k (see Steenrod and Epstein [30]). A polynomial f in P k is called hit if it can be written as a finite sum f = i>0 Sq i (f i ) for some polynomials f i . That means f belongs to A + P k , where A + denotes the augmentation ideal in A. We are interested in the hit problem, set up by F. Peterson, of finding a minimal set of generators for the polynomial algebra P k as a module over the Steenrod algebra. In other words, we want to find a basis of the F 2 -vector spaceThe hit problem was first studied by Peterson [22,23]

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“…Combining the results of Hu'ng [11], Hà [10] and Nam [23], we obtain a complete picture of the behaviour of the rank 4 dual transfer. It should be noted that in [12], Hu'ng and Quỳnh claimed to have a proof that the family { p i : i ≥ 0} is detected by the dual algebraic tranfer, but the details have not appeared.…”

Section: Introductionmentioning

confidence: 93%