We found a match
Your institution may have access to this item. Find your institution then sign in to continue.
- Title
Wargaming with Quadratic Forms and Brauer Configuration Algebras.
- Authors
Moreno Cañadas, Agustín; Fernández Espinosa, Pedro Fernando; Bravo Rios, Gabriel
- 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.
- Subjects
ALGEBRA; SUM of squares; QUADRATIC forms; DYNKIN diagrams; DIRECTED graphs
- Publication
Mathematics (2227-7390), 2022, Vol 10, Issue 5, p729
- ISSN
2227-7390
- Publication type
Article
- DOI
10.3390/math10050729