Torsor

up:: 021 MOC Algebra

“A torsor is like a group that has forgotten its identity.” (John Baez)

In a -torsor, one cannot add elements ─ but rather, one can think of their differences as being elements of an underlying group .

A -torsor is a set with a Group Action over some Group

which is Free and Transitive. This means that every pair of points in has only one element in which “connects” them ─ which can be seen as their difference (or ratio).

Examples

• An Affine Space is an example of an -torsor ─ we can only measure real position differences
• Energies lie in an -torsor ─ we can only measure real energy differences
• Voltages lie in an -torsor ─ we can only measure real voltage differences

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References

• torsor in nLab
• torsors (John Baez)