Loop W(a,b) Lie conformal algebra

Abstract

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.

Conformal biderivations of loop $W(a,b)$ Lie conformal algebra

“…The relations between W (a, b) and CLW(a, b) can be found in [7]. This paper is organized as follows.…”

Infinite rank Schrödinger-Virasoro type Lie conformal algebras

“…Lie conformal algebras [20]. Infinite rank Lie conformal algebras are also important ingredients of Lie conformal algebras, and have also attracted many authors' attention, such as general Lie conformal algebras [3,4,15,17], and some loop Lie conformal algebras [5,8,9,19].…”

“…) is an infinite rank conformal subalgebra, which we call an infinite rank Heisenberg-Virasoro type Lie conformal algebra. The special case CHV (a, 0) is in fact the loop Lie conformal algebra R(1 − a) studied in [9], and the more special case CHV (1, 0) is exactly the loop Heisenberg-Virasoro Lie conformal algebra firstly constructed in [8].…”