Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userFinite irreducible conformal modules over the Lie conformal superalgebra $mathcal{S}(p)$
108
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
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.
rate research
Read More
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.
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.
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.
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 $nge1$.
The loop super-Virasoro conformal superalgebra $mathfrak{cls}$ associated with the loop super-Virasoro algebra is constructed in the present paper. The conformal superderivation algebra of $mathfrak{cls}$ is completely determined, which is shown to consist of inner superderivations. And nontrivial free and free $mathbb{Z}$-graded $mathfrak{cls}$-modules of rank two are classified. We also give a classification of irreducible free $mathfrak{cls}$-modules of rank two and all irreducible submodules of each free $mathbb{Z}$-graded $mathfrak{cls}$-module of rank two.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
