Abstract:This paper classifies complex local representations of the twisted virtual braid group, $TVB_2$, into $\mathrm{GL}_3(\mathbb{C})$. It shows that such representations fall into eight types, all of which are unfaithful and reducible to a two-dimensional representation. Further reducibility to a one-dimensional representation is analyzed for specific types. The paper also examines complex homogeneous local representations of $TVB_n$ into $\mathrm{GL}_{n+1}(\mathbb{C})$ for $n \geq 3$, identifying seven unfaithful types. Additionally, complex local representations of the singular twisted virtual braid group, $STVB_2$, into $\mathrm{M}_3(\mathbb{C})$ are classified into thirteen unfaithful types. Finally, the paper demonstrates that not all complex local extensions of $TVB_2$ representations to $STVB_2$ conform to a $\Phi$-type extension.
From: Mohamad Nasser [view email]
[v1]
Wed, 4 Jun 2025 10:27:00 UTC (114 KB)
[v2]
Wed, 17 Jun 2026 11:56:01 UTC (114 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。