Locally finite basic classical simple Lie superalgebras

TL;DR

This paper investigates the structure of infinite-dimensional Lie superalgebras formed as direct limits of finite-dimensional basic classical simple Lie superalgebras, focusing on their Cartan subalgebras and automorphism groups.

Contribution

It characterizes the conjugacy classes of Cartan subalgebras in these infinite-dimensional superalgebras, extending classical finite-dimensional results.

Findings

Classification of Cartan subalgebras under automorphisms

Description of conjugacy classes in the direct limit setting

Extension of finite-dimensional Lie superalgebra theory

Abstract

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.