Journal of the Ramanujan Mathematical Society

Volume 41, Issue 2, June 2026 pp. 159–172.

The monoid structure of singular twisted virtual braids

Authors: Madeti Prabhakar and Komal Negi
Author institution:Department of Mathematics, Indian Institute of Technology Ropar, Rupnagar 140 001, Punjab, India.

Summary: In this paper, we examine specific submonoids within the singular twisted virtual braid monoid STVB{n}. Notably, we establish that the singular twisted virtual pure braid monoid STVP{n} serves as the kernel of an epimorphism from STVB{n} onto the symmetric group S{n}. We identify the generators and defining relations for STVP{n}. Additionally, we construct other epimorphisms from STVB{n} onto S{n}, whose kernels are analogous to STVP{n}, and determine their respective generators and defining relations. Furthermore, we demonstrate the embedding of the monoid STVB{n} into a group. Also, we provide the extension of the representation of the twisted virtual braid group to the representation of the singular twisted virtual braid monoid.

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