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In this paper, we study deformations and generalized derivations of Lie conformal superalgebras. First, we study conformal derivations of the semidirect product of a Lie conformal superalgebra and its conformal module. Second, we extend the cohomology theory of Lie conformal algebras to the super case and discuss some applications to deformations of Lie conformal superalgebras. Finally, we introduce generalized derivations of Lie conformal superalgebras and study their properties. [ABSTRACT FROM AUTHOR]

In this paper, we classify all finite irreducible conformal modules over a class of Lie conformal algebras W(b) with b∈C related to the Virasoro conformal algebra. Explicitly, any finite irreducible conformal module over W(b) is proved to be isomorphic to MΔ,α,β with Δ≠0 or β≠0 if b = 0, or MΔ,α with Δ≠0 if b≠0. As a byproduct, all finite irreducible conformal modules over the Heisenberg-Virasoro conformal algebra and the W(2, 2) Lie conformal algebra are classified. Finally, the same thing is done for the Schrödinger-Virasoro conformal algebra. [ABSTRACT FROM AUTHOR]

In this paper, we study Lie super-bialgebra and quantization of the super Virasoro algebra, whose even part is the centerless twisted Heisenberg-Virasoro algebra. By using some Liu-Pei-Zhu's results, we prove that all Lie super-bialgebra structures on the super Virasoro algebra are triangular coboundary. Furthermore, we quantize the super Virasoro algebra by the Drinfel'd twist quantization technique and obtain a class of noncommutative and noncocommutative Hopf superalgebras. [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce the notions of Hom Gel'fand-Dorfman bialgebra and Hom-Lie conformal algebra. In this paper, we give four constructions of Hom Gel'fand-Dorfman bialgebras. Also, we provide a general construction of Hom-Lie conformal algebras from Hom-Lie algebras. Finally, we prove that a Hom Gel'fand- Dorfman bialgebra is equivalent to a Hom-Lie conformal algebra of degree 2. [ABSTRACT FROM AUTHOR]