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## Main Question or Discussion Point

This is note about O(3,3) space-time. The related article is:

https://doi.org/10.3390/sym12050817

Here's some background:

In O(3,1) space-time (Minkowski), the six generators of rotations and boosts can form an SU(2) x SU(2) Lie algebra. This algebra is then used generically by all the leptons so that their associated spinors obey special relativity.

In O(3,3) space-time (a mathematical space), the fifteen generators can form a number of SU(2) x SU(2) and related algebras. There are actually enough algebras to allow each lepton in the SM to transform under a unique algebra. This raises two questions, first, is there a one-to-one correspondence between leptons and algebras, and second, if this is true, which leptons are associated with which algebras.

Implications of the article:

The linked article investigates the internal symmetry space of O(3,3). The findings in the article suggest that: mathematical properties and relationships of certain group theory algebras in O(3,3) resemble mathematical properties and relationships of leptons in the SM.

https://doi.org/10.3390/sym12050817

Here's some background:

In O(3,1) space-time (Minkowski), the six generators of rotations and boosts can form an SU(2) x SU(2) Lie algebra. This algebra is then used generically by all the leptons so that their associated spinors obey special relativity.

In O(3,3) space-time (a mathematical space), the fifteen generators can form a number of SU(2) x SU(2) and related algebras. There are actually enough algebras to allow each lepton in the SM to transform under a unique algebra. This raises two questions, first, is there a one-to-one correspondence between leptons and algebras, and second, if this is true, which leptons are associated with which algebras.

Implications of the article:

The linked article investigates the internal symmetry space of O(3,3). The findings in the article suggest that: mathematical properties and relationships of certain group theory algebras in O(3,3) resemble mathematical properties and relationships of leptons in the SM.