Geodesic
Hochschild Cohomology of Polynomial Representations of $\mathrm{GL}_2$
Documenta mathematica, Tome 23 (2018), pp. 117-170.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

We compute the Hochschild cohomology algebras of Ringel-self-dual blocks of polynomial representations of $\mathrm{GL}_2$ over an algebraically closed field of characteristic $p>2$, that is, of any block whose number of simple modules is a power of $p$. These algebras are finite-dimensional and we provide an explicit description of their bases and multiplications.
Classification : 20G05, 16E45
Keywords: Hochschild cohomology, $\mathrm{GL}_2$, Koszul duality, differential graded algebras 
@article{DOCMA_2018__23__a57,
     author = {Miemietz, Vanessa and Turner, Will},
     title = {Hochschild {Cohomology} of {Polynomial} {Representations} of $\mathrm{GL}_2$},
     journal = {Documenta mathematica},
     pages = {117--170},
     publisher = {mathdoc},
     volume = {23},
     year = {2018},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a57/}
}
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Miemietz, Vanessa; Turner, Will. Hochschild Cohomology of Polynomial Representations of $\mathrm{GL}_2$. Documenta mathematica, Tome 23 (2018), pp. 117-170. http://geodesic.mathdoc.fr/item/DOCMA_2018__23__a57/