Geodesic
Enumerations of ideals in niltriangular subalgebra of Chevalley algebras
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 271-277.

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Let $N\Phi(K)$ be the niltriangular subalgebra of Chevalley algebra over a field $K$ associated with a root system $\Phi$. We consider certain non-associative enveloping algebras for some Lie algebra $N\Phi(K)$. We also study the problem of enumeration of standard ideals in algebra $N\Phi(K)$ over any finite field $K;$ for classical Lie types this is the problem which was written earlier (2001).
Keywords: Chevalley algebra, enveloping algebra, ideal.
Mots-clés : niltriangular subalgebra 
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Nikolay D. Hodyunya. Enumerations of ideals in niltriangular subalgebra of Chevalley algebras. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 11 (2018) no. 3, pp. 271-277. http://geodesic.mathdoc.fr/item/JSFU_2018_11_3_a0/

[1] R. Carter, Simple Groups of Lie type, Wiley and Sons, New York, 1972 | MR | Zbl

[2] G.P. Egorychev, V.M. Levchuk, “Enumeration in the Chevalley algebras”, ACM SIGSAM Bulletin, 35:2 (2001), 20–34 | DOI | Zbl

[3] V.M. Levchuk, “Niltriangular subalgebra of Chevalley algebra: the enveloping algebra, ideals and automorphisms”, Dokl. Math., 478:2 (2018) | MR | Zbl

[4] A. Albert, “Power-Associative Rings”, Trans. Amer. Math. Soc., 64:3 (1948), 552–593 | DOI | MR | Zbl

[5] H.C. Myung, “Some Classes of Flexible Lie-Admissible Algebras”, Trans. Amer. Math. Soc., 167 (1972), 79–88 | DOI | MR | Zbl

[6] V.M. Levchuk, “Automorphisms of unipotent subgroups of Chevalley groups”, Algebra and Logic, 29:3 (1990), 211–224 | DOI | MR | Zbl

[7] V.M. Levchuk, G.S. Suleimanova, “Extremal and maximal normal abelian subgroups of a maximal unipotent subgroup in groups of Lie type”, J. Algebra, 349:1 (2012), 98–116 | DOI | MR | Zbl

[8] V.M. Levchuk, “Automorphisms of unipotent subgroups of Lie type groups of small ranks”, Algebra and Logic, 29:2 (1990), 97–112 | DOI | MR | Zbl

[9] N. Bourbaki, Groupes et algebres de Lie, Chapt. IV–VI, Hermann, Paris, 1968 | MR | Zbl

[10] V.P. Krivokolesko, V.M. Levchuk, “Enumeration of ideals in exceptional nilpotent matrix algebras”, Trudy IMM UrO RAN, 21, no. 1, 2015, 166–171 (in Russian) | MR

[11] G.P. Egorychev, “Enumeration of proper $t$-dimensional subspaces of the space $V_m$ over a field $GF(q)$”, Izv. Irkutsk. GU, ser. matem., 17:3 (2016), 12–22 (in Russian) | Zbl

[12] G.S. Suleimanova, Doctor's Dissertation in Mathematics and Physics, SFU, Krasnoyarsk, 2013 (in Russian)

[13] C.A. Athanasiadis, “On a refinement of the generalized Catalan numbers for Weyl groups”, Trans. Amer. Math. Soc., 357:1 (2005), 179–197 | DOI | MR