The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces

Powell, Geoffrey M. L.

doi:10.5802/aif.1773

The structure of the tensor product of

𝔽_{2} [-]

with a finite functor between

𝔽_{2}

-vector spaces

Powell, Geoffrey M. L.

Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805.

Résumé
Abstract

Soit $ℱ$ la catégorie de foncteurs de la catégorie des $𝔽_{2}$ -espaces vectoriels de dimension finie dans la catégorie des $𝔽_{2}$ -espaces vectoriels. Nous étudions la structure du foncteur $I \otimes F \in ℱ$ , où $F$ est un foncteur fini et $I$ désigne le foncteur injectif $V \mapsto 𝔽_{2}^{V^{*}}$ . Un théorème de détection de sous-foncteurs de $I \otimes F$ est démontré, ce qui est la base de la démonstration que le foncteur $I \otimes F$ est artinien de type un.

The paper studies the structure of functors $I \otimes F$ in the category of functors from finite dimensional $𝔽_{2}$ -vector spaces to $𝔽_{2}$ -vector spaces, where $F$ is a finite functor and $I$ is the injective functor $V \mapsto 𝔽_{2}^{V^{*}}$ . A detection theorem is proved for sub-functors of such functors, which is the basis of the proof that the functors $I \otimes F$ are artinian of type one.

MR Zbl | 2 citations dans Numdam

DOI : 10.5802/aif.1773

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     author = {Powell, Geoffrey M. L.},
     title = {The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces},
     journal = {Annales de l'Institut Fourier},
     pages = {781--805},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {3},
     year = {2000},
     doi = {10.5802/aif.1773},
     mrnumber = {2001h:20065},
     zbl = {0958.18006},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1773/}
}

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Powell, Geoffrey M. L. The structure of the tensor product of ${\mathbb {F}}_2[-]$ with a finite functor between ${\mathbb {F}}_2$-vector spaces. Annales de l'Institut Fourier, Tome 50 (2000) no. 3, pp. 781-805. doi : 10.5802/aif.1773. http://www.numdam.org/articles/10.5802/aif.1773/

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