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Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type $ A_1$


Author: Yutaka Yoshii
Journal: Proc. Amer. Math. Soc. 146 (2018), 1977-1989
MSC (2010): Primary 16P10; Secondary 17B45, 20G05, 20G15
DOI: https://doi.org/10.1090/proc/13934
Published electronically: January 29, 2018
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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 $ {\rm SL}_2(k)$, using the primitive idempotents which were constructed before by the author.


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  • [1] 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, https://doi.org/10.1007/s10468-010-9234-6
  • [2] 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, https://doi.org/10.5802/aif.2681
  • [3] 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, https://doi.org/10.1007/s11512-014-0205-8
  • [4] Hirosi Nagao and Yukio Tsushima, Representations of finite groups, translated from the Japanese, Academic Press, Inc., Boston, MA, 1989. MR 998775
  • [5] George B. Seligman, On idempotents in reduced enveloping algebras, Trans. Amer. Math. Soc. 355 (2003), no. 8, 3291-3300. MR 1974688, https://doi.org/10.1090/S0002-9947-03-03314-2
  • [6] Yutaka Yoshii, Primitive idempotents of the hyperalgebra for the $ r$-th Frobenius kernel of $ {\rm SL}(2,k)$, J. Lie Theory 27 (2017), no. 4, 995-1026. MR 3632383

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Additional Information

Yutaka Yoshii
Affiliation: The College of Education, Ibaraki University, 2-1-1 Bunkyo, Mito, Ibaraki, 310-8512, Japan
Email: yutaka.yoshii.6174@vc.ibaraki.ac.jp

DOI: https://doi.org/10.1090/proc/13934
Keywords: Primitive idempotents, projective modules, hyperalgebras.
Received by editor(s): May 10, 2017
Received by editor(s) in revised form: August 23, 2017
Published electronically: January 29, 2018
Communicated by: Kailash Misra
Article copyright: © Copyright 2018 American Mathematical Society

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