Non-Weight Modules over the N = 1 Heisenberg–Virasoro Superalgebra-Reference-Cited by-同舟云学术

Non-Weight Modules over the N = 1 Heisenberg–Virasoro Superalgebra

Published:2024-07-05 Issue:7 Volume:16 Page:853
ISSN:2073-8994
Container-title:Symmetry
language:en
Short-container-title:Symmetry

Author:

Dilxat Munayim¹,Liu Dong²^ORCID

Affiliation:

1. College of Mathematics and System Sciences, Xinjiang University, Urumqi 830046, China

2. Department of Mathematics, Huzhou University, Huzhou 313000, China

Abstract

In this paper, we mainly study free U(h)-modules over the N=1 Heisenberg–Virasoro superalgebra. We construct a family of non-weight modules that are free of rank 2 when regarded as modules over the Cartan subalgebra. Moreover, we classify the free U(h)-modules of rank 2 over the N = 1 Heisenberg–Virasoro superalgebra and provide the necessary and sufficient conditions for such g-modules to be isomorphic.

Funder

Natural Science Foundation of Xinjiang Uygur Autonomous Region

Talent Project of Tianchi Doctoral Program in Xinjiang Uygur Autonomous Region

Publisher

MDPI AG

Link

https://www.mdpi.com/2073-8994/16/7/853/pdf

Reference16 articles.

1. Green, M., Schwarz, J., and Witten, E. (1987). Superstring Theory, Cambridge University Press.

2. Superconformal current algebras and their unitary representations;Kac;Comm. Math. Phys.,1985

3. Beltrami algebra and symmetry of the Belrami equation on Riemann surfaces;Guo;J. Math. Phys.,1990

4. Adamović, D., Jandrić, B., and Radobolja, G. (2019, January 24–29). On the N = 1 Super Heisenberg-Virasoro Vertex Algebra, to Appear in Lie Groups, Number Theory, and Vertex Aglebras. Proceedings of the Conference “Representation Theory XVI”, Dubrovnik, Croatia.

5. The N=1 super Heisenberg-Virasoro vertex algebra at level zero;Radobolja;J. Algebra Appl.,2022