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The Niltriangular Subalgebra of the Chevalley Algebra: the Enveloping Algebra, Ideals, and Automorphisms.
- Source :
-
Doklady Mathematics . Jan2018, Vol. 97 Issue 1, p23-27. 5p. - Publication Year :
- 2018
-
Abstract
- The enveloping algebra of the niltriangular subalgebra <italic>N</italic>Φ(<italic>K</italic>) of the Chevalley algebra of type <italic>A</italic><italic>n</italic>−1 is the algebra of niltriangular <italic>n</italic> × <italic>n</italic> matrices over <italic>K</italic>. The enveloping algebras <italic>R</italic> of other types constructed so far are nonassociative. For classical types, an explicit description of automorphisms of the rings <italic>R</italic> over any commutative associative ring with an identity is given; in the case where <italic>K</italic> is a field, all ideals in <italic>R</italic> are also listed. The enumeration of ideals in <italic>R</italic> for <italic>K</italic> = <italic>GF(q)</italic> leads to a solution of a combinatorial problem concerning ideals of the algebras <italic>N</italic>Φ(<italic>K</italic>). [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*TRIANGLES
*CHEVALLEY groups
*MATRICES (Mathematics)
*ASSOCIATIVE algebras
Subjects
Details
- Language :
- English
- ISSN :
- 10645624
- Volume :
- 97
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Doklady Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 128506167
- Full Text :
- https://doi.org/10.1134/S1064562418010088