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- Title
Enveloping Algebras and Ideals of the Niltriangular Subalgebra of the Chevalley Algebra.
- Authors
Egorychev, G. P.; Levchuk, V. M.; Suleimanova, G. S.; Hodyunya, N. D.
- Abstract
A simple complex Lie algebra is characterized by a root system and a Chevalley basis with the integer structure constants. The well-known arbitrariness of their choice for the niltriangular subalgebra essentially affects the Lie-admissible algebra (in the sense of Albert) over a field such that . We study the uniqueness of the (nonassociative) enveloping algebras of classical types. The enumeration of ideals of the Lie algebras and for leads to the solution of some combinatorial problem listed in ACM SIGSAM Bulletin in 2001. The calculations of multiple combinatorial sums with -binomial coefficient use the integral representation method of combinatorial sums (the coefficient method).
- Subjects
IDEALS (Algebra); ALGEBRA; LIE algebras; INTEGRAL representations; BINOMIAL coefficients; NONASSOCIATIVE algebras
- Publication
Siberian Mathematical Journal, 2023, Vol 64, Issue 2, p300
- ISSN
0037-4466
- Publication type
Article
- DOI
10.1134/S0037446623020052