Wargaming with Quadratic Forms and Brauer Configuration Algebras

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 varia...

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Bibliographic Details
Published inMathematics (Basel) Vol. 10; no. 5; p. 729
Main Authors Moreno Cañadas, Agustín, Fernández Espinosa, Pedro Fernando, Bravo Rios, Gabriel
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.03.2022
Subjects
Brauer configuration algebra
Combinatorics
Defense programs
Dynkin graph
Euclidean geometry
Games
Graph theory
Interception
Missile defense
Missile trajectories
Missiles
mixed sums of triangular and square numbers
path algebra
positive root
quadratic form
Quadratic forms
War games
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Summary: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.
ISSN:2227-7390
2227-7390
DOI:10.3390/math10050729