On some central operators for loop Lie superalgebras

Let g be either a basic classical Lie superalgebra or gl(m, n) over the field of complex numbers C. For any associative, commutative, and finitely generated algebra A with unity, we consider the loop Lie superalgebra g (R) A. In [11], Rao defined a class of central operators for g (R) A and conjectured that these central operators, which generalizes the classical Gelfand invariants, generate the algebra U(g (R) A)g for g = gl(m, n). In this article we prove this conjecture and we also give a spanning set for U(g (R) A)G where g is the orthosymplectic Lie superalgebra and G is the corresponding orthosymplectic supergroup. (c) 2024 Elsevier B.V. All rights reserved.