New simple modules for the Heisenberg-Virasoro algebra
Hongjia Chen,Xiangqian Guo +1 more
TLDR
In this paper, a large class of simple modules for the Heisenberg-Virasoro algebra is constructed, which are determined by the simple modules over the finite-dimensional quotient algebras of certain natural subalgebra.About:
This article is published in Journal of Algebra.The article was published on 2013-09-15 and is currently open access. It has received 42 citations till now. The article focuses on the topics: Projective module & Generalized Verma module.read more
Citations
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Non-weight modules over the Heisenberg–Virasoro algebra and the W algebra W(2,2)
Hongjia Chen,Xiangqian Guo +1 more
TL;DR: In this article, the authors construct and study some non-weight modules for the Heisenberg-Virasoro algebra and the W algebra W(2, 2) whose restriction to the universal enveloping algebra of the degree-0 part (modulo center) is free of rank 1 for these two algebras.
Journal ArticleDOI
Generalized Oscillator Representations of the Twisted Heisenberg-Virasoro Algebra
TL;DR: In this paper, a general result on sufficient conditions for tensor product modules to be simple over an arbitrary Lie algebra was obtained, and the shifting technique was used to determine the necessary and sufficient condition for the tensor products of highest weight modules and modules of intermediate series.
Journal ArticleDOI
A new family of modules over the Virasoro algebra
Hongjia Chen,Xiangqian Guo +1 more
TL;DR: In this article, a new family of Virasoro modules Ω ( λ, α, h ) was constructed, where the non-central Cartan part acts freely of infinite rank.
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Modules over the Heisenberg-Virasoro and $W(2,2)$ algebras
Hongjia Chen,Xiangqian Guo +1 more
TL;DR: In this article, the authors consider the modules for the Heisenberg-Virasoro algebra and the W algebra and determine the modules whose restriction to the Cartan subalgebra (modulo center) are free of rank $1$ for the two algebras.
Journal ArticleDOI
Quasi-Whittaker modules for the Schrödinger algebra ☆
TL;DR: In this article, a class of quasi-Whittaker modules for the Schrodinger algebra S was proposed, which is induced by the Borel subalgebra of S related with the triangular decomposition.
References
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Book
Introduction to Lie Algebras and Representation Theory
TL;DR: In this paper, Semisimple Lie Algebras and root systems are used for representation theory, isomorphism and conjugacy theorem, and existence theorem for representation.
Book
Infinite Dimensional Lie Algebras
TL;DR: The invariant bilinear form and the generalized casimir operator are integral representations of Kac-Moody algebras and the weyl group as mentioned in this paper, as well as a classification of generalized cartan matrices.
Book
Bombay Lectures on Highest Weight Representations of Infinite Dimensional Lie Algebras
Victor G. Kac,A. K. Raina +1 more
TL;DR: A collection of a series of lectures given by Prof. V Kac at the Tata Institute, India in Dec '85 and Jan '86 is presented in this article, where the authors focus on the idea of a highest weight representation, which goes through four different incarnations.
Journal ArticleDOI
Moduli Spaces of Curves and Representation Theory
TL;DR: In this article, a canonical isomorphism between the second coho- mology of the Lie algebra of regular differential operators on (Cx of degree 1) and the second singular cohomology of moduli space of curves of genus g is established.
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