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).

DERIVATIONS OF THE EVEN PARTS FOR MODULAR LIE SUPERALGEBRAS OF CARTAN TYPE W AND S

2007 ◽  
Vol 17 (04) ◽  
pp. 661-714 ◽  
Author(s):  
WENDE LIU ◽  
YONGZHENG ZHANG
Keyword(s):  
Lie Algebras ◽  
Lie Superalgebra ◽  
Adjoint Representation ◽  
Lie Superalgebras ◽  
Base Field ◽  
Characteristic P ◽  
Derivation Algebra ◽  
Finite Dimensional ◽  
Outer Derivation ◽  
Generator Sets

Let 𝔽 be the underlying base field of characteristic p < 3 and denote by [Formula: see text] and [Formula: see text] the even parts of the finite-dimensional generalized Witt Lie superalgebra W and the special Lie superalgebra S, respectively. We first give the generator sets of the Lie algebras [Formula: see text] and [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text] and [Formula: see text], we then determine the derivation algebra of [Formula: see text] and the derivation space of [Formula: see text] to [Formula: see text], where [Formula: see text] is viewed as a [Formula: see text]-module by means of the adjoint representation. As a result, we describe explicitly the derivation algebra of [Formula: see text]. Furthermore, we prove that the outer derivation algebras of [Formula: see text] and [Formula: see text] are abelian Lie algebras or metabelian Lie algebras with explicit structure. In particular, we give the dimension formulas of the derivation algebras and outer derivation algebras of [Formula: see text] and [Formula: see text]. Thus, we may make a comparison between the even parts of the (outer) superderivation algebras of W and S and the (outer) derivation algebras of the even parts of W and S, respectively.

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

The Even Part of Finite-Dimensional Modular Lie Superalgebra Γ

2021 ◽  
Vol 28 (03) ◽  
pp. 479-496
Author(s):  
Yusi Fan ◽  
Xiaoning Xu ◽  
Liangyun Chen
Keyword(s):  
Lie Algebra ◽  
Lie Superalgebra ◽  
Base Field ◽  
Modular Lie Superalgebra ◽  
Derivation Algebra ◽  
Finite Dimensional ◽  
Generator Sets

Let [Formula: see text] be the underlying base field of characteristic [Formula: see text] and denote by [Formula: see text] the even part of the finite-dimensional Lie superalgebra [Formula: see text]. We give the generator sets of the Lie algebra [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text], we describe explicitly the derivation algebra of [Formula: see text].

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).

QUANTUM HAMILTONIAN REDUCTION AND WB ALGEBRA

1992 ◽  
Vol 07 (20) ◽  
pp. 4885-4898 ◽  
Author(s):  
KATSUSHI ITO
Keyword(s):  
Lie Algebras ◽  
Free Field ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Hamiltonian Reduction ◽  
Affine Lie Algebras ◽  
Quantum Hamiltonian Reduction ◽  
Free Field Realization ◽  
Coset Construction ◽  
Quantum Hamiltonian

We study the quantum Hamiltonian reduction of affine Lie algebras and the free field realization of the associated W algebra. For the nonsimply laced case this reduction does not agree with the usual coset construction of the W minimal model. In particular, we find that the coset model [Formula: see text] can be obtained through the quantum Hamiltonian reduction of the affine Lie superalgebra B(0, n)(1). To show this we also construct the Feigin-Fuchs representation of affine Lie superalgebras.

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