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Wargaming with Quadratic Forms and Brauer Configuration Algebras.
- Source :
- Mathematics (2227-7390); Mar2022, Vol. 10 Issue 5, p729, 1p
- Publication Year :
- 2022
-
Abstract
- Recently, Postnikov introduced Bert Kostant's game to build the maximal positive root associated with the quadratic form of a simple graph. This result, and some other games based on Cartan matrices, give a new version of Gabriel's theorem regarding algebras classification. In this paper, as a variation of Bert Kostant's game, we introduce a wargame based on a missile defense system (MDS). In this case, missile trajectories are interpreted as suitable paths of a quiver (directed graph). The MDS protects a region of the Euclidean plane by firing missiles from a ground-based interceptor (GBI) located at the point (0 , 0) . In this case, a missile success interception occurs if a suitable positive number associated with the launches of the enemy army can be written as a mixed sum of triangular and square numbers. [ABSTRACT FROM AUTHOR]
- Subjects :
- ALGEBRA
SUM of squares
QUADRATIC forms
DYNKIN diagrams
DIRECTED graphs
Subjects
Details
- Language :
- English
- ISSN :
- 22277390
- Volume :
- 10
- Issue :
- 5
- Database :
- Complementary Index
- Journal :
- Mathematics (2227-7390)
- Publication Type :
- Academic Journal
- Accession number :
- 155706988
- Full Text :
- https://doi.org/10.3390/math10050729