Representations of the General Linear Lie Superalgebra in the BGG Category $$\mathcal{O}$$

2014 ◽  
pp. 71-98 ◽  
Author(s):  
Jonathan Brundan
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
General Linear Lie Superalgebra

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 Z2×Z2-graded general linear Lie superalgebra

2020 ◽  
Vol 61 (1) ◽  
pp. 011702
Author(s):  
Phillip S. Isaac ◽  
N. I. Stoilova ◽  
Joris Van der Jeugt
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
General Linear Lie Superalgebra

scholarly journals The Kac–Wakimoto character formula for the general linear Lie superalgebra

2015 ◽  
Vol 9 (6) ◽  
pp. 1419-1452 ◽  
Author(s):  
Michael Chmutov ◽  
Crystal Hoyt ◽  
Shifra Reif
Keyword(s):  
Lie Superalgebra ◽  
Character Formula ◽  
General Linear ◽  
General Linear Lie Superalgebra

scholarly journals Super tableaux and a branching rule for the general linear Lie superalgebra

2014 ◽  
Vol 63 (2) ◽  
pp. 274-282 ◽  
Author(s):  
Sean Clark ◽  
Yung-Ning Peng ◽  
S. Kuang Thamrongpairoj
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
Branching Rule ◽  
General Linear Lie Superalgebra

scholarly journals Equivalence of Blocks for the General Linear Lie Superalgebra

2013 ◽  
Vol 103 (12) ◽  
pp. 1313-1327 ◽  
Author(s):  
Shun-Jen Cheng ◽  
Volodymyr Mazorchuk ◽  
Weiqiang Wang
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
General Linear Lie Superalgebra

scholarly journals Yangian of the General Linear Lie Superalgebra

2020 ◽  
Author(s):  
Maxim Nazarov ◽  
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
Basic Properties ◽  
General Linear Lie Superalgebra

We prove several basic properties of the Yangian of the Lie superalgebra gl(M|N).

scholarly journals Uncolouring of Lie colour algebras

1997 ◽  
Vol 55 (3) ◽  
pp. 425-452 ◽  
Author(s):  
D. S. McAnally ◽  
A. J. Brakcen
Keyword(s):  
Lie Superalgebra ◽  
General Linear ◽  
Baxter Equation

The link between a Lie colour algebra and a corresponding Lie superalgebra is clarified in the case of the general linear algebras. The Lie superalgebra inherits from the colour cocommutative coproduct of the corresponding Lie colour algebra, a super coproduct which differs from the usual one, and is not supercocommutative. It is associated with a new R-matrix satisfying the super Yang-Baxter equation.

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