Do you want to publish a course? Click here

Irreducible Jet modules for the vector field Lie algebra on $mathbb{S}^1times mathbb{C}$

114   0   0.0 ( 0 )
 Added by Genqiang Liu
 Publication date 2020
  fields
and research's language is English




Ask ChatGPT about the research

For a commutative algebra $A$ over $mathbb{C}$,denote $mathfrak{g}=text{Der}(A)$. A module over the smash product $A# U(mathfrak{g})$ is called a jet $mathfrak{g}$-module, where $U(mathfrak{g})$ is the universal enveloping algebra of $mathfrak{g}$.In the present paper, we study jet modules in the case of $A=mathbb{C}[t_1^{pm 1},t_2]$.We show that $A#U(mathfrak{g})congmathcal{D}otimes U(L)$, where $mathcal{D}$ is the Weyl algebra $mathbb{C}[t_1^{pm 1},t_2, frac{partial}{partial t_1},frac{partial}{partial t_2}]$, and $L$ is a Lie subalgebra of $A# U(mathfrak{g})$ called the jet Lie algebra corresponding to $mathfrak{g}$.Using a Lie algebra isomorphism $theta:L rightarrow mathfrak{m}_{1,0}Delta$, where $mathfrak{m}_{1,0}Delta$ is the subalgebra of vector fields vanishing at the point $(1,0)$, we show that any irreducible finite dimensional $L$-module is isomorphic to an irreducible $mathfrak{gl}_2$-module. As an application, we give tensor product realizations of irreducible jet modules over $mathfrak{g}$ with uniformly bounded weight spaces.



rate research

Read More

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.
131 - Ming Ding , Jie Xiao , Fan Xu 2008
The canonical bases of cluster algebras of finite types and rank 2 are given explicitly in cite{CK2005} and cite{SZ} respectively. In this paper, we will deduce $mathbb{Z}$-bases for cluster algebras for affine types $widetilde{A}_{n,n},widetilde{D}$ and $widetilde{E}$. Moreover, we give an inductive formula for computing the multiplication between two generalized cluster variables associated to objects in a tube.
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.
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 this paper, the property and the classification the simple Whittaker modules for the schr{o}dinger algebra are studied. A quasi-central element plays an important role in the study of Whittaker modules of level zero. For the Whittaker modules of nonzero level, our arguments use the Casimir element of semisimple Lie algebra $sl_2$ and the description of simple modules over conformal Galilei algebras by R. L{u}, V. Mazorchuk and K. Zhao.
comments
Fetching comments Fetching comments
Sign in to be able to follow your search criteria
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا