Geodesic
Unitary Harish-Chandra Modules over Block Type Lie Algebras B(q)
Hongjia Chen1 ; Xiangqian Guo2
1School of Mathematical Sciences, University of Science and Technology, Hefei 230026, Anhui, P. R. China
2Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China
Journal of Lie Theory, Tome 23 (2013) no. 3, pp. 827-836

Voir la notice de l'article provenant de la source Heldermann Verlag

For any nonzero complex number q, there is a Lie algebra of Block type, denoted by q. In this paper, we classify the unitary Harish-Chandra modules for these algebras. We first give a description of conjugate-linear anti-involutions on q. Then we obtain the sufficient and necessary conditions for irreducible uniformly bounded unitary Harish-Chandra modules and irreducible unitary highest (lowest) weight Harish-Chandra modules.
Classification : 17B10, 17B20, 17B65, 17B66, 17B68
Mots-clés : Block type algebra, Virasoro algebra, Harish-Chandra module, intermediate series module

Hongjia Chen  1   ; Xiangqian Guo  2

1 School of Mathematical Sciences, University of Science and Technology, Hefei 230026, Anhui, P. R. China
2 Department of Mathematics, Zhengzhou University, Zhengzhou 450001, Henan, P. R. China 
Hongjia Chen; Xiangqian Guo. Unitary Harish-Chandra Modules over Block Type Lie Algebras B(q). Journal of Lie Theory, Tome 23 (2013) no. 3, pp. 827-836. http://geodesic.mathdoc.fr/item/JOLT_2013_23_3_a12/
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     author = {Hongjia Chen and Xiangqian Guo},
     title = {Unitary {Harish-Chandra} {Modules} over {Block} {Type} {Lie} {Algebras} {B(q)}},
     journal = {Journal of Lie Theory},
     pages = {827--836},
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