Advanced search
Publication Cover
Linear and Multilinear Algebra Volume 70, 2022 - Issue 22
Submit an article Journal homepage
93
Views
1
CrossRef citations to date
0
Altmetric
Research Article

Irreducible tensor product modules over the affine-Virasoro algebra of type A1

Qiu-Fan ChenDepartment of Mathematics, Shanghai Maritime University, Shanghai, People's Republic of ChinaView further author information
&
Yu-Feng YaoDepartment of Mathematics, Shanghai Maritime University, Shanghai, People's Republic of ChinaCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-9469-2030View further author information
ORCID Icon
Pages 7558-7574 | Received 22 Aug 2021, Accepted 20 Oct 2021, Published online: 07 Nov 2021

References

  • Kac V. Highest weight representations of conformal current algebras. In Symposium on Topological and Geometric Methods in Field Theory. Espoo, Finland: World Scientific; 1986. p. 3–16.
  • Kuroki G. Fock space representations of an affine Lie algebras and integral representations in the Wess–Zumino–Witten models. Commun Math Phys. 1991;142(3):511–542.
  • Billig Y. A category of modules for the full toroidal Lie algebra. Int Math Res Not. 2006;2006;46pp.
  • Eswara Rao S, Jiang C. Classification of irreducible integrable representations for the full toroidal Lie algebras. J Pure Appl Algebra. 2005;200:71–85.
  • Jiang C, You H. Irreducible representations for the affine-Virasoro Lie algebras of type Bl. Chinese Ann Math Ser B. 2004;25(3):359–368.
  • Liu G, Lü R, Zhao K. A class of simple weight Virasoro modules. J Algebra. 2015;424:506–521.
  • Liu D, Pei Y, Xia L. Classification of quasi-finite irreducible modules over affine-Virasoro algebras. J Lie Theory. 2021;31(2):575–582.
  • Liu X, Qian M. Bosonic Fock representations of the affine-Virasoro algebra. J Phys A. 1994;27(5):131–136.
  • Xia L, Hu N. Irreducible representations for Virasoro-toroidal Lie algebras. J Pure Appl Algebra. 2004;194:213–237.
  • Cheng S, Lam N. Finite conformal modules over the N = 2, 3, 4 superconformal algebras. J Math Phys. 2001;42(2):906–933.
  • Gao Y, Hu N, Liu D. Representations of the affine-Virasoro algebra of type A1. J Geom Phys. 2016;106:102–107.
  • Batra P, Mazorchuk V. Blocks and modules for Whittaker pairs. J Pure Appl Algebra. 2011;215:1552–1568.
  • Cai Y, Tan H, Zhao K. Module structure on U(h) for Kac–Moody algebras (in Chinese). Sci Sin Math. 2017;47(11):1491–1514.
  • Cai Y, Zhao K. Module structure on U(h) for basic Lie superalgebras. Toyama Math J. 2015;37:55–72.
  • Han J, Chen Q, Su Y. Modules over the algebras Vir(a,b). Linear Algebra Appl. 2017;515:11–23.
  • Mazorchuk V, Weisner E. Simple Virasoro modules induced from codimension one subalgebras of the positive part. Proc Am Math Soc. 2012;142(11):3695–3703.
  • Mazorchuk V, Zhao K. Simple Virasoro modules which are locally finite over a positive part. Selecta Math (N.S.). 2014;20(3):839–854.
  • Nilsson J. Simple sln+1-module structures on U(h). J Algebra. 2015;424:294–329.
  • Nilsson J. U(h)-free modules and coherent families. J Pure Appl Algebra. 2016;220:1475–1488.
  • Tan H, Zhao K. Wn+ and Wn-module structures on U(hn). J Algebra. 2015;424:257–375.
  • Chen Q, Han J. Non-weight modules over the affine-Virasoro algebra of type A1. J Math Phys. 2019;60:071707.
  • Chen H, Guo X. Tensor product weight modules over the Virasoro algebra. J Lond Math Soc. 2013;88:829–844.
  • Chen H, Han J, Su Y, et al. Two classes of non-weight modules over the twisted Heisenberg-Virasoro algebra. Manuscripta Math. 2019;160(1–2):265–284.
  • Guo X, Liu X, Wang J. New irreducible tensor product modules for the Virasoro algebra. 2020;24(2):191–206.
  • Tan H, Zhao K. Irreducible Virasoro modules from tensor products. Ark Mat. 2016;54:181–200.
  • Zhang H. A class of representations over the Virasoro algebra. J Algebra. 1997;190:1–10.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.