Primitive idempotents of the hyperalgebra for the $r$-th Frobenius kernel of ${\rm SL}(2,k)$
In this paper we construct primitive idempotents of the hyperalgebra for the $r$-th Frobenius kernel of the algebraic group ${\rm SL}(2,k)$.
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arXiv subjects
Yutaka Yoshii
Publications and source records attributed to Yutaka Yoshii.
Projective modules for the subalgebra of degree 0 in a finite-dimensional hyperalgebra of type $A_1$
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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Generating sets of the Jacobson radical of the hyperalgebra of (SL$_2$)$_r$
We give generating sets of the Jacobson radical of the hyperalgebra of the $r$-th Frobenius kernel of the algebraic group ${\rm SL}_2$ over an algebraically closed field of characteristic $p>0$. This result generalizes earlier work by Wong for $r=1$ and odd $p$.
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Certain linear isomorphisms for hyperalgebras relative to a Chevalley group
Let $G$ be a simply connected and simple algebraic group defined and split over a finite prime field $\mathbb{F}_p$ of $p$ elements. In this paper, using an $\mathbb{F}_p$-linear map splitting Frobenius endomorphism on a hyperalgebra relative to $G$, we obtain some $\mathbb{F}_p$-linear isomorphisms induced by multiplication in the hyperalgebra.
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Some results on certain finite-dimensional subalgebras of the hyperalgebra of a universal Chevalley group
In the hyperalgebra of the $r$-th Frobenius kernel of a universal Chevalley group over a field of characteristic $p>0$, we study some subsets and the subalgebras generated by them and give some results. We are particularly interested in the case that $p$ is 'very small' and the Dynkin diagram is not simply-laced.
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A basis of a certain module for the hyperalgebra $({\rm SL}_2)_r$ and some applications
In the hyperalgebra $\mathcal{U}_r$ of the $r$-th Frobenius kernel $({\rm SL}_2)_r$ of the algebraic group ${\rm SL}_2$, we construct a basis of the $\mathcal{U}_r$-module generated by a certain element which was given by the author before. As its applications, we also prove some results on the $\mathcal{U}_r$-modules and the algebra $\mathcal{U}_r$.
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