ترغب بنشر مسار تعليمي؟ اضغط هنا

Finite irreducible conformal modules of rank two Lie conformal algebras

182   0   0.0 ( 0 )
 نشر من قبل Yanyong Hong
 تاريخ النشر 2021
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

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.

قيم البحث

اقرأ أيضاً

107 - Maosen Xu , Yanyong Hong 2021
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.
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 mod ules 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 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 intermedi ate 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.
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 $nge1$.
111 - Yucai Su , Xiaoqing Yue 2021
In a previous paper by the authors, we obtain the first example of a finitely freely generated simple $mathbb Z$-graded Lie conformal algebra of linear growth that cannot be embedded into any general Lie conformal algebra. In this paper, we obtain, a s a byproduct, another class of such Lie conformal algebras by classifying $mathbb Z$-graded simple Lie conformal algebras ${cal G}=oplus_{i=-1}^infty{cal G}_i$ satisfying the following, (1) ${cal G}_0cong{rm Vir}$, the Virasoro conformal algebra; (2) Each ${cal G}_i$ for $ige-1$ is a ${rm Vir}$-module of rank one. These algebras include some Lie conformal algebras of Block type.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا