Notes on Actions of Sets and Groups and Generalized Affine Spaces
Dan Jonsson
TL;DR
This paper surveys various notions related to group actions, including new and existing concepts, and explores their use in generalizing affine spaces, viewing actions as functions into transformation monoids.
Contribution
It introduces a generalized framework for affine spaces based on group actions and transformation monoids, unifying and extending existing notions.
Findings
Provides a comprehensive survey of group action concepts
Introduces a generalized model of affine spaces using transformation monoids
Connects group actions with affine space generalizations
Abstract
Some well-known and less well-known or new notions related to group actions are surveyed. Some of these notions are used to generalize affine spaces. Actions are seen as functions with values in transformation monoids
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Advanced Topology and Set Theory