Generalized Heisenberg-Virasoro algebras (Q1042544)

The authors introduce the generalized Heisenberg-Virasoro algebra, which is a generalization of the twisted Heisenberg-Virasoro Lie algebra \(H_{\text{Vir}}\) from the integer ring \(\mathbb Z\) to an additive subgroup \(M\) of a field \(\mathbb F\). For the exact definition see Section 2 (Definition 1) of the paper. In Section 3, they prove that the generalized Heisenberg-Virasoro algebra is the universal extension of the Lie algebra of generalized differential operators on a circle of order at least one: \(L = \mathbb F\{t^x\partial, t^y\mid x, y\in A, \partial\in T\}\). In Sections 4 and 5, they determine derivations and automorphisms of the generalized Heisenberg-Virasoro algebra.