Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type 𝐴₁

Yoshii, Yutaka

doi:10.1090/proc/13934

Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type $A_1$
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Proc. Amer. Math. Soc. 146 (2018), 1977-1989 Request permission

Abstract:

We describe the structure of projective indecomposable modules for the subalgebra consisting of the elements of degree 0 in the hyperalgebra of the $r$-th Frobenius kernel for the algebraic group $\textrm {SL}_2(k)$, using the primitive idempotents which were constructed before by the author.

References

Michel Gros, A splitting of the Frobenius morphism on the whole algebra of distributions of $SL_2$, Algebr. Represent. Theory 15 (2012), no. 1, 109–118. MR 2872483, DOI 10.1007/s10468-010-9234-6
Michel Gros and Masaharu Kaneda, Contraction par Frobenius de $G$-modules, Ann. Inst. Fourier (Grenoble) 61 (2011), no. 6, 2507–2542 (2012) (French, with English and French summaries). MR 2976319, DOI 10.5802/aif.2681
Michel Gros and Masaharu Kaneda, Un scindage du morphisme de Frobenius quantique, Ark. Mat. 53 (2015), no. 2, 271–301 (French, with English and French summaries). MR 3391172, DOI 10.1007/s11512-014-0205-8
Hirosi Nagao and Yukio Tsushima, Representations of finite groups, Academic Press, Inc., Boston, MA, 1989. Translated from the Japanese. MR 998775
George B. Seligman, On idempotents in reduced enveloping algebras, Trans. Amer. Math. Soc. 355 (2003), no. 8, 3291–3300. MR 1974688, DOI 10.1090/S0002-9947-03-03314-2
Yutaka Yoshii, Primitive idempotents of the hyperalgebra for the $r$-th Frobenius kernel of $\textrm {SL}(2,k)$, J. Lie Theory 27 (2017), no. 4, 995–1026. MR 3632383