Geodesic
Distributions over an algebra of truncated polynomial
Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 187-205 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study integrable distributions over the $K$-algebra $\mathscr O_n$ of truncated polynomials, where $K$ is a field of characteristic $p>0$. We obtain an analogue of the theorem of Frobenius; we describe the equivalence classes of $TI$-distributions, i.e., of those distributions $\mathscr L$ with respect to which the algebra $\mathscr O_n$ has no nontrivial $\mathscr L$-invariant ideals; we show that over a perfect field any $TI$-distribution is equivalent to a general Lie algebra of Cartan type $W_s(\mathscr F)$; and we find all the forms of the Zassenhaus algebra, in the process making essential use of the theory of representations of the chromatic quiver $_\circ\overrightarrow{_\rightsquigarrow}_\circ$ of Kronecker. Bibliography: 13 titles. 
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     author = {M. I. Kuznetsov},
     title = {Distributions over an algebra of truncated polynomial},
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     volume = {64},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1989_64_1_a11/}
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M. I. Kuznetsov. Distributions over an algebra of truncated polynomial. Sbornik. Mathematics, Tome 64 (1989) no. 1, pp. 187-205. http://geodesic.mathdoc.fr/item/SM_1989_64_1_a11/

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