Filtered Lie conformal algebras whose associated graded algebras are isomorphic to that of general conformal algebra gc1

JOURNAL OF ALGEBRA

卷:340

Article

Su, Yucai^1,2  Yue, Xiaoqing¹ 

[1] Tongji Univ, Dept Math, Shanghai 200092, Peoples R China

[2] Univ Sci & Technol China, Wu Wen Tsun Key Lab Math, Hefei 230026, Peoples R China

关键词: Lie conformal algebras;    Filtered algebras;    General conformal algebras;    Second cohomology groups;   

DOI  :  10.1016/j.jalgebra.2011.06.001

来源: Elsevier

【 摘 要 】

Let G be a filtered Lie conformal algebra whose associated graded conformal algebra is isomorphic to that of general conformal algebra gc(1). In this paper, we prove that G congruent to gc(1) or gr gc(1) (the associated graded conformal algebra of gc(1)), by making use of some results on the second cohomology groups of the conformal algebra g with coefficients in its module M-b,M-0 of rank 1, where g = Vir proportional to M-a,M-0 is the semi-direct sum of the Virasoro conformal algebra Vir with its module M-a,M-0. Furthermore, we prove that gr gc(1) does not have a nontrivial representation on a finite C[partial derivative]-module, this provides an example of a finitely freely generated simple Lie conformal algebra of linear growth that cannot be embedded into the general conformal algebra gC(N) for any N. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free