The exterior algebra and central notions in mathematics
Gunnar Fl{\o}ystad
TL;DR
This paper surveys how the exterior algebra and its modifications underpin key concepts across combinatorics, topology, Lie theory, physics, and algebraic geometry, highlighting their foundational role in diverse mathematical areas.
Contribution
It provides a comprehensive overview of the central importance of exterior algebra and its variants in multiple core mathematical disciplines.
Findings
Exterior algebra underpins key concepts in combinatorics and topology.
Deformations and quotients of exterior algebra reveal new structures in Lie theory and physics.
The survey highlights the unifying role of exterior algebra across various mathematical fields.
Abstract
This note surveys how the exterior algebra and deformations or quotients of it, gives rise to centrally important notions in five domains of mathematics: Combinatorics, Topology, Lie theory, Mathematical physics, and Algebraic geometry.
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