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The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms

Abstract

The enveloping algebra of the niltriangular subalgebra NΦ(K) of the Chevalley algebra of type An−1 is the algebra of niltriangular n × n matrices over K. The enveloping algebras R of other types constructed so far are nonassociative. For classical types, an explicit description of automorphisms of the rings R over any commutative associative ring with an identity is given; in the case where K is a field, all ideals in R are also listed. The enumeration of ideals in R for K = GF(q) leads to a solution of a combinatorial problem concerning ideals of the algebras NΦ(K).

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Correspondence to V. M. Levchuk.

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Original Russian Text © V.M. Levchuk, 2018, published in Doklady Akademii Nauk, 2018, Vol. 478, No. 2, pp. 137–140.

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Levchuk, V.M. The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms. Dokl. Math. 97, 23–27 (2018). https://doi.org/10.1134/S1064562418010088

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  • DOI: https://doi.org/10.1134/S1064562418010088