Locally finite basic classical simple Lie superalgebras

Document Type : Research Paper

Author

1 Department of Mathematics‎, ‎University of Isfahan‎, ‎Isfahan‎, ‎Iran‎, ‎P.O‎. ‎Box 81745-163

2 School of Mathematics‎, ‎Institute for Research in‎ ‎Fundamental‎ ‎Sciences (IPM)‎, ‎P.O‎. ‎Box 19395-5746‎, ‎Tehran‎, ‎Iran.

Abstract

In this work, we study direct limits of finite dimensional basic classical simple Lie superalgebras and obtain the conjugacy classes of Cartan subalgebras under the group of automorphisms.

Keywords

Main Subjects


B. Allison, S. Azam, S. Berman, Y. Gao and A. Pianzola, Extended affine Lie algebras
and their root systems, Mem. Amer. Math. Soc. 126 (1997), no. 603, 122 pages.
B. Allison, S. Berman, J. Faulkner and A. Pianzola, Multiloop realization of extended affine lie algebras and lie tori, Trans. Amer. Math. Soc. 361 (2009), no. 9, 4807--4842.
S. Berman and R. Moody, Lie algebras graded by finite root systems and the intersection matrix algebras of Slodowy, Invent. Math. 108 (1992), no. 2, 323--347.
R. Carter, Lie Algebras of Finite and Affine Type, Cambridge Stud. Adv. Math. 96, Cambridge Univ. Press, Cambridge, 2005.
R. Høegh-Krohn and B. Torresani, Classification and construction of quasi-simple Lie algebras, J. Funct. Anal. 89 (1990) 106--136.
J.E. Humphreys, Introduction to Lie Algebras and Representation Theory, Springer Verlag, New York, 1972.
K. Iohara and Y. Koga, Central extensions of Lie superalgebras, Comment. Math. Helv. 86 (2011), no. 4, 985--986.
O. Loos and E. Neher, Locally finite root systems, Mem. Amer. Math. Soc. 171 (2004), no. 811, 214 pages.
R.V. Moody and A. Pianzola, Lie Algebras with Triangular Decompositions, John Wiley & Sons, New York, 1995.
K.H. Neeb and N. Stumme, The classification of locally finite split simple Lie algebras, J. Reine angew. Math. 533 (2001) 25--53.
E. Neher, Extended affine Lie algebras and other generalizations of affine Lie algebras-a survey, Developments and Trends in Infinite-Dimensional Lie Theory, pp. 53--126, Progr. Math. 228, Birkhauser Boston, Inc., Boston, MA, 2011.
J.W. Van de Leur, A classification of contragredient Lie superalgebras of finite growth, Comm. Algebra 17 (1989), no. 8, 1815--1841.
M. Yousofzadeh, Extended affine root supersystems, J. Algebra 449 (2016) 539--564.
M. Yousofzadeh, Extended affine Lie superalgebras, Publ. Res. Inst. Math. Sci. 52 (2016), no. 3, 309--333.
M. Yousofzadeh, Locally finite root supersystems, Comm. Algebra, to appear.
M. Yousofzadeh, Locally finite basic classical Lie superalgebras, Arxiv:1502.04586v1 [math.QA].