Loop Schrödinger–Virasoro Lie conformal algebra

Abstract

In this paper, we introduce two kinds of Lie conformal algebras associated with the loop Schrödinger-Virasoro Lie algebra and the extended loop Schrödinger-Virasoro Lie algebra, respectively. The conformal derivations, the second cohomology groups of these two conformal algebras are completely determined. And nontrivial free conformal modules of rank one and Z-graded free intermediate series modules over these two conformal algebras are also classified in the present paper.

Finite irreducible conformal modules over the extended Block type Lie conformal algebra $\mathfrak{B}(α,β,p)$

“…But, the theory of infinite Lie conformal algebra is relatively backward. Some interesting examples of infinite Lie conformal algebras were constructed by closely linked infinite-dimensional loop Lie algebras, such as loop Virasoro Lie conformal algebra, loop Heisneberg-Virasoro Lie conformal algebra, loop Schrödinger-Virasoro Lie conformal algebra (see, e.g., [6,10,20]). One of the most important examples of infinite simple conformal algebras is the general Lie conformal algebra gc N , which plays the same important role in the theory of Lie conformal algebras as the general Lie algebra gl N does in the theory of Lie algebras.…”

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].…”

“…Note that the special case CSV (1, 0) is exactly the loop Schrödinger-Virasoro Lie conformal algebra recently studied in [5]. In addition, CSV (a, b) contains many important conformal subalgebras.…”

A new class of Z-graded Lie conformal algebras of infinite rank

“…One well-known way of constructing of these Lie conformal algebras is to consider loop algebras of Lie algebras (cf. [4,7,10,16]). In this paper we construct a new class of Z-graded Lie conformal algebras of infinite rank, which contains the loop Virasoro Lie conformal algebra [16] and the Block type Lie conformal algebra [11].…”