Irreducible modules over the Lie conformal algebra {\mathfrak {B}}(\alpha ,\beta ,p)

• Chen, Haibo ^[1] ; Su, Yucai ^[1] ; Hong, Yanyong ^[2]
  1. [1] Jimei University

     Jimei University

     China

     
  2. [2] Hangzhou Normal University

     Hangzhou Normal University

     China

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 76, Fasc. 3, 2025, págs. 613-626
• Idioma: inglés
• DOI: 10.1007/s13348-024-00448-6
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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 {\mathbb {Z}}-graded free intermediate 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 ,\beta \in {\mathbb {C}}, p\in {\mathbb {C}}^*. As an application, the classifications of finite irreducible conformal modules over a series of finite Lie conformal algebras {\mathfrak {b}}(n) for {\mathfrak {b}}(n) are given.

• Referencias bibliográficas
  • Barakat, A., De sole, A., Kac, V.G.: Poisson vertex algebras in the theory of Hamiltonian equations. Jpn. J. Math. 4, 141–252 (2009)
  • Bakalov, B., Kac, V.G., Voronov, A.A.: Cohomology of conformal algebras. Commun. Math. Phys. 200, 561–598 (1999)
  • Boyallian, C., Meinardi, V.: Finite growth representations of conformal Lie algebras that contain a Virasoro subalgebra. J. Algebra 388, 141–159...
  • Belavin, A., Polyakov, A., Zamolodchikov, A.: Infinite conformal symmetry in two dimensional quantum field theory. Nucl. Phys. B 241, 333–380...
  • Boyallian, C., Kac, V.G., Liberati, J.I.: On the classification of subalgebras of Cend_N and gc_N. J. Algebra 260, 32–63 (2003)
  • Chen, H., Han, J., Su, Y., Xu, Y.: Loop Schrödinger–Virasoro Lie conformal algebra. Int. J. Math. 27, 1650057 (2016)
  • Cheng, S., Kac, V.G.: Conformal modules. Asian J. Math. 1, 181–193 (1997)
  • Cheng, S., Kac, V.G., Wakimoto, M.: Extensions of conformal modules. In: Topological Field Theory, Primitive Forms and Related Topics(Kyoto),...
  • D’Andrea, A., Kac, V.G.: Structure theory of finite conformal algebras. Sel. Math. 4, 377–418 (1998)
  • Fan, G., Su, Y., Wu, H.: Loop Heisenberg–Virasoro Lie conformal algebra. J. Math. Phys. 55, 123508 (2014)
  • Hong, Y., Wu, Z.: Simplicity of quadratic Lie conformal algebras. Commun. Algebra 45, 141–150 (2017)
  • Kac, V.G.: Vertex algebras for beginners. University Lecture Series, vol. 10. American Mathematical Society (1996)
  • Kac, V.G.: Formal distribution algebras and conformal algebras. In: XIIth International Congress of Mathematical Physics (ICMP ’97) (Brisbane),...
  • Kac, V.G.: The idea of locality. In: Doebner, H.-D., et al. (eds.) Physical Applications and Mathematical Aspects of Geometry, Groups and...
  • Luo, L., Hong, Y., Wu, Z.: Finite irreducible modules of Lie conformal algebras {\cal{W} }(a, b) and some Schrödinger–Virasoro type Lie conformal...
  • Su, Y.: Low dimensional cohomology of general conformal algebras gc_N. J. Math. Phys. 45, 509–524 (2004)
  • Su, Y., Xia, C., Yuan, L.: Classification of finite irreducible conformal modules over a class of Lie conformal algebras of Block type. J....
  • Su, Y., Yuan, L.: Schrödinger–Virasoro Lie conformal algebra. J. Math. Phys. 54, 053503 (2013)
  • Su, Y., Yue, X.: Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra gc_1....
  • Wu, H., Chen, Q., Yue, X.: Loop Virasoro Lie conformal algbera. J. Math. Phys. 55, 011706 (2014)
  • Wu, H., Yuan, L.: Classification of finite irreducible conformal modules over some Lie conformal algebras related to the Virasoro conformal...
  • Xia, C.: Classification of finite irreducible conformal modules over Lie conformal superalgebras of Block type. J. Algebra 531, 141–164 (2019)
  • Yuan, L., Ling, K.: Extensions of Schrödinger–Virasoro conformal modules. Commun. Algebra 47, 2883–2903 (2019)