The Bogomolov multiplier of Lie superalgebras

TL;DR

This paper extends the concept of the Bogomolov multiplier to Lie superalgebras, computes it for specific classes like Heisenberg and low-dimensional real Lie superalgebras, and explores related extensions.

Contribution

It introduces the Bogomolov multiplier for Lie superalgebras and calculates it for key examples, advancing understanding of their structure and invariants.

Findings

Computed the Bogomolov multiplier for Heisenberg Lie superalgebras

Determined the multiplier for real Lie superalgebras of dimension ≤ 4

Extended the notion of commutativity preserving extensions to superalgebras

Abstract

In this paper, we extend the notion of the Bogomolov multiplier and the commutativity preserving extension to Lie superalgebras. Moreover, we compute the Bogomolov multiplier of Heisenberg and real Lie superalgebras of dimension at most $4$.