Extended affine Lie superalgebras containing Cartan subalgebras

2019 ◽  
Vol 532 ◽  
pp. 61-79
Author(s):  
Malihe Yousofzadeh
Keyword(s):  
Lie Superalgebras ◽  
Cartan Subalgebras

scholarly journals Simple Modules for Modular Lie SuperalgebrasW(0∣n),S(0∣n), andK(n)

2015 ◽  
Vol 2015 ◽  
pp. 1-8
Author(s):  
Zhu Wei ◽  
Qingcheng Zhang ◽  
Yongzheng Zhang ◽  
Chunyue Wang
Keyword(s):  
Positive Root ◽  
Sufficient Conditions ◽  
Lie Superalgebras ◽  
Prime Characteristic ◽  
Simple Modules ◽  
Cartan Subalgebras ◽  
Modular Lie Superalgebras

This paper constructs a series of modules from modular Lie superalgebrasW(0∣n),S(0∣n), andK(n)over a field of prime characteristicp≠2. Cartan subalgebras, maximal vectors of these modular Lie superalgebras, can be solved. With certain properties of the positive root vectors, we obtain that the sufficient conditions of these modules are irreducibleL-modules, whereL=W(0∣n),S(0∣n), andK(n).

scholarly journals Irreducible modules with highest weight vectors over modular Witt and special Lie superalgebras

2019 ◽  
Vol 17 (1) ◽  
pp. 1381-1391
Author(s):  
Keli Zheng ◽  
Yongzheng Zhang
Keyword(s):  
Lie Superalgebras ◽  
Arbitrary Field ◽  
Special Linear ◽  
Highest Weight ◽  
Irreducible Modules

Abstract Let 𝔽 be an arbitrary field of characteristic p > 2. In this paper we study irreducible modules with highest weight vectors over Witt and special Lie superalgebras of 𝔽. The same irreducible modules of general and special linear Lie superalgebras, which are the 0-th part of Witt and special Lie superalgebras in certain ℤ-grading, are also considered. Then we establish a certain connection called a P-expansion between these modules.

scholarly journals Primitive ideals, twisting functors and star actions for classical Lie superalgebras

2016 ◽  
Vol 2016 (718) ◽  
Author(s):  
Kevin Coulembier ◽  
Volodymyr Mazorchuk
Keyword(s):  
Representation Theory ◽  
Lie Superalgebras ◽  
Simple Modules ◽  
Primitive Ideals

AbstractWe study three related topics in representation theory of classical Lie superalgebras. The first one is classification of primitive ideals, i.e. annihilator ideals of simple modules, and inclusions between them. The second topic concerns Arkhipov’s twisting functors on the BGG category

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