Conformal modules and their extensions of a Lie conformal algebra related to a 2-dimensional Novikov algebra

2019/07/03 by Yuan, Lamei, Wang, Yanjie
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1907.02960

Abstract

Let R be a free Lie conformal algebra of rank 2 with ℂ[∂]-basis \L,I\ and relations [L_λ L]=(∂+2 λ) (L+I), [L_λ I]=(∂+λ) I, [I_λ L]=λI, [I_λ I]=0. In this paper, we first classify all finite nontrivial irreducible conformal modules over R. Then we determine extensions between two finite irreducible conformal R-modules.

Related

• Extensions of modules over a class of Lie conformal algebras W(b)
• Extensions of finite irreducible modules over rank two Lie conformal algebra
• Classification of rank two Lie conformal algebras
• Finite irreducible modules of a class of ℤ⁺-graded Lie conformal algebras
• Classification of finite irreducible conformal modules over N=2 Lie conformal superalgebras of Block type