Email this article The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms
- Authors: Levchuk V.M.1
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Affiliations:
- Institute of Mathematics and Computer Science
- Issue: Vol 97, No 1 (2018)
- Pages: 23-27
- Section: Mathematics
- URL: https://journals.rcsi.science/1064-5624/article/view/225448
- DOI: https://doi.org/10.1134/S1064562418010088
- ID: 225448
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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).
About the authors
V. M. Levchuk
Institute of Mathematics and Computer Science
Author for correspondence.
Email: vlevchuk@sfu-kras.ru
Russian Federation, Krasnoyarsk, 660041
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