Eigenvalues of Casimir operators for the general linear and orthosymplectic Lie superalgebras

1983 ◽  
Vol 24 (11) ◽  
pp. 2546-2549 ◽  
Author(s):  
Adam M. Bincer
Keyword(s):  
Lie Superalgebras ◽  
General Linear ◽  
Casimir Operators

Double Derivations of n-Lie Superalgebras

2018 ◽  
Vol 25 (01) ◽  
pp. 161-180
Author(s):  
Bing Sun ◽  
Liangyun Chen ◽  
Xin Zhou
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
General Linear ◽  
Base Field ◽  
Inner Derivation ◽  
Derivation Algebra ◽  
General Linear Lie Superalgebra

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).

scholarly journals The Brundan–Kazhdan–Lusztig conjecture for general linear Lie superalgebras

2015 ◽  
Vol 164 (4) ◽  
pp. 617-695 ◽  
Author(s):  
Shun-Jen Cheng ◽  
Ngau Lam ◽  
Weiqiang Wang
Keyword(s):  
Lie Superalgebras ◽  
General Linear
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