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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3 Pith papers cite this work. Polarity classification is still indexing.
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Introduces multi-welded twin groups M_kWT_n, establishes quotient maps and structural properties including abelianization and perfect commutator subgroup for n≥5, and classifies homogeneous 2-local and 3-local representations.
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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Multi-welded twin groups
Introduces multi-welded twin groups M_kWT_n, establishes quotient maps and structural properties including abelianization and perfect commutator subgroup for n≥5, and classifies homogeneous 2-local and 3-local representations.
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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.