Universal virtual and welded braid groups are constructed to unify prior variants, with classifications of their complex homogeneous local representations and proofs of abelianization, perfect commutator, trivial center, and finite quotients.
Nasser,Insights on the homogeneous3-local representations of the twin groups, J
2 Pith papers cite this work. Polarity classification is still indexing.
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The multi-virtual twin group M_kVT_n admits exactly eight distinct homogeneous 2-local representations into GL_n(C) for n >= 3; these are generally unfaithful but irreducible under explicit conditions, with induced non-local representations constructed for the pure subgroup.
citing papers explorer
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On Universal Virtual and Welded Braid Groups and Their Linear Representations
Universal virtual and welded braid groups are constructed to unify prior variants, with classifications of their complex homogeneous local representations and proofs of abelianization, perfect commutator, trivial center, and finite quotients.
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Presentations and Representations of the Multi-Virtual Twin Group and Associated Subgroups
The multi-virtual twin group M_kVT_n admits exactly eight distinct homogeneous 2-local representations into GL_n(C) for n >= 3; these are generally unfaithful but irreducible under explicit conditions, with induced non-local representations constructed for the pure subgroup.