论文标题
矩阵理论中的外部代数
Exterior algebras in matroid theory
论文作者
论文摘要
订购的蓝图是概括单体和有序半序的代数对象，$ \ mathbb {f} _1^{\ pm} $ - 代数为blueprints，其具有元素$ε$的蓝图，该元素可作为$ -1 $ $ -1 $。在这项工作中，我们为$ \ mathbb {f} _1^{\ pm} $ - 代数介绍了外部代数的类似物，该代数为Matroid提供了新的隐态性。如果$ \ mathbb {f} _1^{\ pm} $ - algebra来自戒指，我们还展示了如何恢复通常的外部代数，如果$ \ mathbb {f} f} _1^{\ pm} $ - algebra来自idemp。
Ordered blueprints are algebraic objects that generalize monoids and ordered semirings, and $\mathbb{F}_1^{\pm}$-algebras are ordered blueprints that have an element $ε$ that acts as $-1$. In this work we introduce an analogue of the exterior algebra for $\mathbb{F}_1^{\pm}$-algebras that provides a new cryptomorphism for matroids. We also show how to recover the usual exterior algebra if the $\mathbb{F}_1^{\pm}$-algebra comes from a ring, and the Giansiracusa Grassmann algebra if the $\mathbb{F}_1^{\pm}$-algebra comes from an idempotent semifield.
