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A class of simple Lie algebras attached to unit forms.
- Source :
-
Frontiers of Mathematics in China . Aug2017, Vol. 12 Issue 4, p787-803. 17p. - Publication Year :
- 2017
-
Abstract
- Let n ≥ 3. The complex Lie algebra, which is attached to a unit form q( x , x ,..., x ) = $${\sum\nolimits_{i = 1}^n {x_i^2 + \sum\nolimits_{1 \leqslant i \leqslant j \leqslant n} {\left( { - 1} \right)} } ^{j - i}}{x_i}{x_j}$$ and defined by generators and generalized Serre relations, is proved to be a finite-dimensional simple Lie algebra of type A, and realized by the Ringel-Hall Lie algebra of a Nakayama algebra of radical square zero. As its application of the realization, we give the roots and a Chevalley basis of the simple Lie algebra. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 16733452
- Volume :
- 12
- Issue :
- 4
- Database :
- Academic Search Index
- Journal :
- Frontiers of Mathematics in China
- Publication Type :
- Academic Journal
- Accession number :
- 123652017
- Full Text :
- https://doi.org/10.1007/s11464-016-0616-x