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Register a new userFinite irreducible conformal modules over the extended Block type Lie conformal algebra $mathfrak{B}(alpha,beta,p)$
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In this paper, we introduce a class of infinite Lie conformal algebras $mathfrak{B}(alpha,beta,p)$, which are the semi-direct sums of Block type Lie conformal algebra $mathfrak{B}(p)$ and its non-trivial conformal modules of $Z$-graded free intermediate series. The annihilation algebras are a class of infinite-dimensional Lie algebras, which include a lot of interesting subalgebras: Virasoro algebra, Block type Lie algebra, twisted Heisenberg-Virasoro algebra and so on. We give a complete classification of all finite non-trivial irreducible conformal modules of $mathfrak{B}(alpha,beta,p)$ for $alpha,betainC, pinC^*$. As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras $mathfrak{b}(n)$ for $ngeq1$ are given.
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In the present paper, we introduce a class of infinite Lie conformal superalgebras $mathcal{S}(p)$, which are closely related to Lie conformal algebras of extended Block type defined in cite{CHS}. Then all finite non-trivial irreducible conformal modules over $mathcal{S}(p)$ for $pinC^*$ are completely classified. As an application, we also present the classifications of finite non-trivial irreducible conformal modules over finite quotient algebras $mathfrak{s}(n)$ for $ngeq1$ and $mathfrak{sh}$ which is isomorphic to a subalgebra of Lie conformal algebra of $N=2$ superconformal algebra. Moreover, as a generalized version of $mathcal{S}(p)$, the infinite Lie conformal superalgebras $mathcal{GS}(p)$ are constructed, which have a subalgebra isomorphic to the finite Lie conformal algebra of $N=2$ superconformal algebra.
In the present paper, we prove that any finite non-trivial irreducible module over a rank two Lie conformal algebra $mathcal{H}$ is of rank one. We also describe the actions of $mathcal{H}$ on its finite irreducible modules explicitly. Moreover, we show that all finite non-trivial irreducible modules of finite Lie conformal algebras whose semisimple quotient is the Virasoro Lie conformal algebra are of rank one.
Let $L$ be a Lie algebra of Block type over $C$ with basis ${L_{alpha,i},|,alpha,iinZ}$ and brackets $[L_{alpha,i},L_{beta,j}]=(beta(i+1)-alpha(j+1))L_{alpha+beta,i+j}$. In this paper, we shall construct a formal distribution Lie algebra of $L$. Then we decide its conformal algebra $B$ with $C[partial]$-basis ${L_alpha(w),|,alphainZ}$ and $lambda$-brackets $[L_alpha(w)_lambda L_beta(w)]=(alphapartial+(alpha+beta)lambda)L_{alpha+beta}(w)$. Finally, we give a classification of free intermediate series $B$-modules.
We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over ${frak {B}}(p)$ may be a nontrivial extension of a finite conformal module over ${frak {Vir}}$ if $p=-1$, where ${frak {Vir}}$ is a Virasoro conformal subalgebra of ${frak {B}}(p)$. As a byproduct, we also obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal algebras ${frak b}(n)$ for $nge1$.
In this paper, we introduce the notion of completely non-trivial module of a Lie conformal algebra. By this notion, we classify all finite irreducible modules of a class of $mathbb{Z}^+$-graded Lie conformal algebras $mathcal{L}=bigoplus_{i=0}^{infty} mathbb{C}[partial]L_i$ satisfying $ [{L_0}_lambda L_0]=(partial+2lambda)L_0,$ and $[{L_1}_lambda L_i] eq 0$ for any $iin mathbb{Z}^+$. These Lie conformal algebras include Block type Lie conformal algebra $mathcal{B}(p)$ and map Virasoro Lie conformal algebra $mathcal{V}(mathbb{C}[T])=Virotimes mathbb{C}[T]$. As a result, we show that all non-trivial finite irreducible modules of these algebras are free of rank one as a $mathbb{C}[partial]$-module.
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