Homological algebra/Topology
Some extension groups between exponential functors

Presented by: Michèle Vergne

Quyet, Nguyen Le Chi1
1 Department of Mathematics & Informatics, Ho Chi Minh City University of Education, Viet Nam
Comptes Rendus. Mathématique, Volume 357 (2019) no. 9, pp. 693-696.

Let F be the category of functors that send a finite-dimensional vector space over F2 to a vector space over F2. In this note, we describe the first extension groups between some exponential functors such as ExtF1(S⁎,Λ⁎), ExtF1(S4⁎,Λ⁎), and ExtF1(S4⁎,S4⁎), where S⁎, Λ⁎, S4⁎ are the symmetric power, the exterior power, and the truncated symmetric power at the power 4, respectively. Three main techniques are used: tri-graded Hopf algebra structure of the extension groups between two exponential functors, the polynomial filtration of these functors, and the hypercohomology spectral sequences.

Soit F la catégorie des foncteurs depuis la catégorie des F2-espaces vectoriels de dimension finie vers celle des F2-espaces vectoriels. Dans cette note, nous décrivons les premiers groupes d'extensions entre certains foncteurs exponentiels tels que ExtF1(S⁎,Λ⁎), ExtF1(S4⁎,Λ⁎) et ExtF1(S4⁎,S4⁎), où S⁎, Λ⁎, S4⁎ sont respectivement la puissance symétrique, la puissance extérieure et la puissance symétrique tronquée à la puissance 4. Trois techniques principales sont utilisées : la structure d'algèbre de Hopf tri-graduée des groupes d'extensions entre deux foncteurs exponentiels, la filtration polynomiale de ces foncteurs et les suites spectrales d'hypercohomologie.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2019.09.005
Quyet, Nguyen Le Chi 1

1 Department of Mathematics & Informatics, Ho Chi Minh City University of Education, Viet Nam 
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Quyet, Nguyen Le Chi. Some extension groups between exponential functors. Comptes Rendus. Mathématique, Volume 357 (2019) no. 9, pp. 693-696. doi : 10.1016/j.crma.2019.09.005. http://archive.numdam.org/articles/10.1016/j.crma.2019.09.005/

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