2-gerbes and 2-Tate spaces

TL;DR

This paper constructs a central extension of automorphism groups of 2-Tate vector spaces using 2-gerbes, enabling the definition of central extensions of double loop groups, advancing the understanding of higher categorical structures in algebra.

Contribution

It introduces a novel construction of central extensions for automorphism groups of 2-Tate spaces via 2-gerbes, linking higher category theory with loop group extensions.

Findings

Constructed a central extension of automorphism groups of 2-Tate spaces.

Defined central extensions of double loop groups using 2-gerbes.

Established a new framework connecting 2-gerbes with higher loop group structures.

Abstract

We construct a central extension of the group of automorphisms of a 2-Tate vector space viewed as a discrete 2-group. This is done using an action of this 2-group on a 2-gerbe of gerbel theories. This central extension is used to define central extensions of double loop groups.