Let HV be the loop Heisenberg-Virasoro Lie algebra over C with basisIn this paper, a formal distribution Lie algebra of HV is constructed. Then the associated conformal algebra CHV is studied, where CHV has a C[∂ ]-basisIn particular, the conformal derivations of CHV are determined. Finally, rank one conformal modules and Z-graded free intermediate series modules over CHV are classified.

In this paper we attempt to investigate the super-biderivations of Lie superalgebras. Furthermore, we prove that all super-biderivations on the centerless super-Virasoro algebras are inner super-biderivations. Finally, we study the linear super commuting maps on the centerless super-Virasoro algebras.

Let R be a Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra CDer(R), the conformal quasiderivation algebra QDer(R) and the generalized conformal derivation algebra GDer(R). The generalized conformal derivation algebra is a natural generalization of the conformal derivation algebra. Obviously, we have the following toweris the general Lie conformal algebra. Furthermore, we mainly research the connection of these generalized conformal derivations. Finally, the conformal (α, β , γ)-derivations of Lie conformal algebras are studied. Moreover, we obtain some connections between several specific generalized conformal derivations and the conformal (α, β , γ)-derivations. In addition, all conformal (α, β , γ)-derivations of finite simple Lie conformal algebras are characterized.In this section, for the reader's convenience, we shall summarize some basic facts about Lie conformal algebras used in this paper, see [4,8,9]. Definition 2.1. A Lie conformal algebra R is an A -module endowed with a C-bilinear map

Fix a, b ∈ C, let LW (a, b) be the loop W (a, b) Lie algebra over C with basisIn this paper, a formal distribution Lie algebra of LW (a, b) is constructed. Then the associated conformal algebra CLW (a, b) is studied, whereIn particular, we determine the conformal derivations and rank one conformal modules of this conformal algebra. Finally, we study the central extensions and extensions of conformal modules.

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The derivation algebras, automorphism groups and second cohomology groups of the generalized loop Schrödinger-Virasoro algebras are completely determined in this paper.

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