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DOI: 10.23671/VNC.2015.2.7278

Niltriangular subalgebras of the Chevalley algebras and their generalizations

Levchuk V. M. , Litavrin A. V. , Hodyunya N. D. , Tsigankov V. V.
Vladikavkaz Mathematical Journal 2015. Vol. 17. Issue 2.
We study some problems concerned with ideals and automorphisms of niltriangular subalgebras of classical Lie type Chevalley algebras  over a field \(K\) and of their non-finitary generalizations and also automorphisms of adjoint group. We characterize (for Lie type \(A_ {n-1})\) every Lie ideal of algebra \(NT(n, K)\) of all niltriangular \(n \times n\) matrices by a selection of constants from \(K\). When \(K = GF(q)\), this gives a combinatorial expression of number of Lie ideals and, for a simple \(q\), also the number of normal subgroups in unitriangular group \(UT(n,q)\).
Keywords: Chevalley algebra, niltriangular subalgebra, non-finitary generalizations, maximal abelian ideals, automorphisms, adjoint group
Language: Russian Download the full text  
For citation: Levchuk V. M., Litavrin A. V., Hodyunya N. D.,† Tsigankov V. V. Niltriangular subalgebras of the Chevalley algebras and their† generalizations. Vladikavkazskii matematicheskii zhurnal [Vladikavkaz Math. J.], vol. 17, no. 2, pp.37-46. DOI 10.23671/VNC.2015.2.7278
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