Wargaming with Quadratic Forms and Brauer Configuration Algebras

被引：1

作者：

Moreno Canadas, Agustin ^{[1
]}

Espinosa, Pedro Fernando Fernandez ^{[1
]}

Bravo Rios, Gabriel ^{[1
]}

机构：

[1] Univ Nacl Colombia, Dept Matemat, Edificio Yu Takeuchi 404, Kra 30 45-03, Bogota, Colombia

来源：

MATHEMATICS | 2022年 / 10卷 / 05期

关键词：

Brauer configuration algebra; Dynkin graph; mixed sums of triangular and square numbers; path algebra; positive root; quadratic form; quiver representation; wargame; MIXED SUMS; SQUARES; NUMBER;

D O I：

10.3390/math10050729

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：19