Abstract Grassmannians are of fundamental importance in projective geometry, algebraic geometry, and representation theory. A vast literature has grown up using many different languages of higher mathematics, such as multilinear and tensor algebra, matroid theory, and Lie groups and Lie algebras. Here we explore the Plucker relations in Clifford's geometric algebra. We discover that the Plucker relations can be fully characterized in terms of the geometric product, without the need for a confusing hodgepodge of many different formalisms and mathematical traditions found in the literature.

中文翻译：

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几何代数中Plücker关系的注记

摘要 Grassmannians 在射影几何、代数几何和表示论中具有重要的意义。大量文献已经使用多种不同的高等数学语言发展起来，例如多线性和张量代数、拟阵理论以及李群和李代数。在这里，我们探索克利福德几何代数中的普拉克关系。我们发现 Plucker 关系可以根据几何乘积来完全表征，而无需将文献中的许多不同形式主义和数学传统混为一谈。