Loop Virasoro Lie Conformal Algebra

Abstract

The Lie conformal algebra of loop Virasoro algebra, denoted by $\mathcal{CW}$, is introduced in this paper. Explicitly, $\mathcal{CW}$ is a Lie conformal algebra with $\mathbb{C}[\partial ]$-basis $\{L_i|i\in \mathbb{C}\}$ and $\lambda$-brackets $[L_i{}_{\lambda }{L}_j]=(-\partial -2\lambda )L_{i+j}$. Then conformal derivations of $\mathcal{CW}$ are determined. Finally, rank one conformal modules and $\mathbb{Z}$-graded free intermediate series modules over $\mathcal{CW}$ are classified.

10 pages

References in corpus (1)

• The Lie conformal algebra of a Block type Lie algebra

Cited by in corpus (12)

• Loop Heisenberg-Virasoro Lie Conformal algebra
• Infinite rank Schrodinger-Virasoro type Lie conformal algebras
• Central extensions and conformal derivations of a class of Lie conformal algebras
• Finite irreducible conformal modules over the Lie conformal superalgebra $\mathcal{S}(p)$
• A new Composition-Diamond lemma for associative conformal algebras
• A new Composition-Diamond lemma for dialgebras
• Structures of $W(2,2)$ Lie conformal algebra
• Loop super-Virasoro Lie conformal superalgebra
• Generalized conformal derivations of Lie conformal algebras
• Loop W(a,b) Lie conformal algebra
• Another class of simple graded Lie conformal algebras that cannot be embedded into general Lie conformal algebras
• Structure of a class of Lie conformal algebras of Block type