frobenius lie algebra
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2021 ◽  
pp. 1-12
Author(s):  
Vincent E. Coll ◽  
Nicholas Mayers ◽  
Nicholas Russoniello

2021 ◽  
Vol 12 (1) ◽  
pp. 59-69
Author(s):  
Henti Henti ◽  
Edi Kurniadi ◽  
Ema Carnia

In this paper, we study the quasi-associative algebra property for the real Frobenius  Lie algebra  of dimension 18. The work aims  to prove that  is a quasi-associative algebra and to compute its formulas explicitly. To achieve this aim, we apply the literature reviews method corresponding to Frobenius Lie algebras, Frobenius functionals, and the structures of quasi-associative algebras. In the first step, we choose a Frobenius functional determined by direct computations of a bracket matrix of  and in the second step, using an induced symplectic structure, we obtain the explicit formulas of quasi-associative algebras for . As the results, we proved that  has the quasi-associative algebras property, and we gave their formulas explicitly. For future research, the case of the quasi-associative algebras on   is still an open problem to be investigated. Our result can motivate to solve this problem.  


2020 ◽  
Vol 4 (2) ◽  
pp. 107
Author(s):  
Edi Kurniadi

In the present paper, we study some properties of the Heisenberg Lie algebra of dimension . The main purpose of this research is to construct a real Frobenius Lie algebra from the Heisenberg Lie algebra of dimension . To achieve this, we exhibit  how to compute the derivation of the Heisenberg Lie algebra by following Oom’s result. In this research, we use a literature review method to some related papers corresponding to a derivation of a Lie algebra, Frobenius Lie algebras, and Plancherel measure. Determining a conjecture of a real Frobenius Lie algebra is obtained. As the main result, we prove that conjecture. Namely, for the given the Heisenberg Lie algebra, there exists a commutative subalgebra of dimension one such that its semi direct sum is a real Frobenius Lie algebra of dimension . Futhermore, in the notion of the Lie group of the Heisenberg Lie algebra which is called the Heisenberg Lie group, we compute the generalized character of its group  and we determine the Plancherel measure of the unitary dual of the Heisenberg Lie group. As our contributions, we complete some examples of Frobenius Lie algebras obtained from a nilpotent Lie algebra and we also give alternative computations to find the Plancherel measure of the Heisenberg Lie group.


2020 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Edi Kurniadi

 In this paper we study that any derivation of affine Lie algebra of dimension 6, denoted by ,  is inner. We give another approach to prove it by direct computations of transformation matrix of derivation of . We show that transformation matrix for the derivation of any element in  equals to  transformation matrix of adjoint representation of its element. Furthermore, we  give an alternative to prove that  is Frobenius Lie algebra. Keywords :Affine Lie algebra, Derivation of a Lie algebra, Frobenius Lie algebra


2009 ◽  
Vol 88 (1-3) ◽  
pp. 333-341 ◽  
Author(s):  
Murray Gerstenhaber ◽  
Anthony Giaquinto

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