On the defining relations of the affine Lie superalgebras and their quantized universal enveloping superalgebras

TL;DR

This paper establishes explicit defining relations for affine Lie superalgebras and their quantized universal enveloping superalgebras, including Drinfeld's realizations, enabling precise algebraic descriptions.

Contribution

It provides the first complete set of defining relations for affine Lie superalgebras and their quantum counterparts, including Drinfeld's realizations.

Findings

Explicit defining relations for affine Lie superalgebras

Explicit defining relations for affine quantized superalgebras

Drinfeld's realizations of quantum affine superalgebras

Abstract

In this paper, we give defining relations of the affine Lie superalgebras an and defining relations of a super-version of the Drinfeld[D]-Jimbo[J] affine quantized universal enveloping algebras. As a result, we can exactly define the affine quantized universal enveloping superalgebras with generators and relations. Moreover we give a Drinfeld's realizations of $U_h({\hat {sl}}(m|n)^{(1)})$.