Heisenberg Group
A three-dimensional Lie group of zero curvature whose coordinates can be understood as (x, y, area). Its multiplication includes cross terms, and the commutator equals the signed area spanned by two vectors, making it useful for recording the order of events.
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The Event2Vec library provides several non-commutative or geometrized alternative spaces: hyperbolic space (Möbius addition), the κ-stereographic model, spherical space (SO(n) rotations), and the Heisenberg group.
The Heisenberg group is a three-dimensional zero-curvature Lie group whose coordinates can be understood as (x, y, area), whose multiplication contains a cross term, and whose commutator equals the signed area spanned by the two vectors, which can be used to record order information.
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The Event2Vec library provides several non-commutative or geometrized alternative spaces: hyperbolic space (Möbius addition), the κ-stereographic model, spherical space (SO(n) rotations), and the Heisenberg group.
50%UnverifiedThe Heisenberg group is a three-dimensional zero-curvature Lie group whose coordinates can be understood as (x, y, area), whose multiplication contains a cross term, and whose commutator equals the signed area spanned by the two vectors, which can be used to record order information.
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