Virtual braid groups of type B and weak categorification

TL;DR

This paper introduces virtual braid groups of type B and establishes a connection to invertible complexes of bimodules, advancing the understanding of their algebraic and categorical structures.

Contribution

It defines virtual braid groups of type B and constructs a morphism to isomorphism classes of invertible bimodule complexes, providing a new categorical perspective.

Findings

Defined virtual braid groups of type B

Constructed a morphism to bimodule complexes

Established foundational categorical structures

Abstract

We define virtual braid groups of type B and construct a morphism from such a group to the group of isomorphism classes of some invertible complexes of bimodules up to homotopy.