scholarly journals The classification of 5-dimensional p-nilpotent restricted Lie algebras over perfect fields, I

2016 ◽  
Vol 464 ◽  
pp. 97-140 ◽  
Author(s):  
Iren Darijani ◽  
Hamid Usefi
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras

scholarly journals The classification of p-nilpotent restricted Lie algebras of dimension at most 4

2016 ◽  
Vol 28 (4) ◽  
Author(s):  
Csaba Schneider ◽  
Hamid Usefi
Keyword(s):  
Lie Algebras ◽  
Restricted Lie Algebras

AbstractIn this paper we obtain the classification of

Representations of restricted Lie algebras and families of associative ℒ-algebras

1999 ◽  
Vol 1999 (507) ◽  
pp. 189-218 ◽  
Author(s):  
Alexander Premet ◽  
Serge Skryabin
Keyword(s):  
Linear Function ◽  
Lie Algebras ◽  
Associative Algebra ◽  
Maximal Dimension ◽  
Closed Field ◽  
Enveloping Algebra ◽  
Restricted Lie Algebra ◽  
Restricted Lie Algebras ◽  
Support Varieties

Abstract Let ℒ be an n-dimensional restricted Lie algebra over an algebraically closed field K of characteristic p > 0. Given a linear function ξ on ℒ and a scalar λ ∈ K, we introduce an associative algebra Uξ,λ (ℒ) of dimension pn over K. The algebra Uξ,1 (ℒ) is isomorphic to the reduced enveloping algebra Uξ (ℒ), while the algebra Uξ,0 (ℒ) is nothing but the reduced symmetric algebra Sξ (ℒ). Deformation arguments (applied to this family of algebras) enable us to derive a number of results on dimensions of simple ℒ-modules. In particular, we give a new proof of the Kac-Weisfeiler conjecture (see [41], [35]) which uses neither support varieties nor the classification of nilpotent orbits, and compute the maximal dimension of simple ℒ-modules for all ℒ having a toral stabiliser of a linear function.

scholarly journals Capable n-Lie algebras and the classification of nilpotent n-Lie algebras with s(A)=3

2016 ◽  
Vol 110 ◽  
pp. 25-29 ◽  
Author(s):  
Hamid Darabi ◽  
Farshid Saeedi ◽  
Mehdi Eshrati
Keyword(s):  
Lie Algebras

scholarly journals Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic

1985 ◽  
Vol 38 (3) ◽  
pp. 330-350 ◽  
Author(s):  
D. F. Holt ◽  
N. Spaltenstein
Keyword(s):  
Finite Field ◽  
Lie Algebras ◽  
Closed Field ◽  
Nilpotent Orbits ◽  
Reductive Algebraic Group ◽  
Exceptional Lie Algebras ◽  
Closed Fields ◽  
Characteristic 3 ◽  
Algebraically Closed Fields

AbstractThe classification of the nilpotent orbits in the Lie algebra of a reductive algebraic group (over an algebraically closed field) is given in all the cases where it was not previously known (E7 and E8 in bad characteristic, F4 in characteristic 3). The paper exploits the tight relation with the corresponding situation over a finite field. A computer is used to study this case for suitable choices of the finite field.

Complete classification of pseudo H-type Lie algebras: I

2017 ◽  
Vol 190 (1) ◽  
pp. 23-51 ◽  
Author(s):  
Kenro Furutani ◽  
Irina Markina
Keyword(s):  
Lie Algebras ◽  
Complete Classification

scholarly journals On classification of (n+6)-dimensional nilpotent n-Lie algebras of class 2 with n≥4

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Mehdi Jamshidi ◽  
Farshid Saeedi ◽  
Hamid Darabi
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Design Methodology ◽  
Central Element ◽  
Complete Understanding ◽  
Content Type ◽  
Low Dimension

PurposeThe purpose of this paper is to determine the structure of nilpotent (n+6)-dimensional n-Lie algebras of class 2 when n≥4.Design/methodology/approachBy dividing a nilpotent (n+6)-dimensional n-Lie algebra of class 2 by a central element, the authors arrive to a nilpotent (n+5) dimensional n-Lie algebra of class 2. Given that the authors have the structure of nilpotent (n+5)-dimensional n-Lie algebras of class 2, the authors have access to the structure of the desired algebras.FindingsIn this paper, for each n≥4, the authors have found 24 nilpotent (n+6) dimensional n-Lie algebras of class 2. Of these, 15 are non-split algebras and the nine remaining algebras are written as direct additions of n-Lie algebras of low-dimension and abelian n-Lie algebras.Originality/valueThis classification of n-Lie algebras provides a complete understanding of these algebras that are used in algebraic studies.

scholarly journals k-step nilpotent Lie algebras

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Michel Goze ◽  
Elisabeth Remm
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Deformation Process ◽  
Nilpotent Lie Algebras ◽  
Early Stages ◽  
Finite Dimensional ◽  
Contraction Process ◽  
Finite Dimensional Lie Algebras

AbstractThe classification of complex or real finite dimensional Lie algebras which are not semi simple is still in its early stages. For example, the nilpotent Lie algebras are classified only up to dimension 7. Moreover, to recognize a given Lie algebra in the classification list is not so easy. In this work, we propose a different approach to this problem. We determine families for some fixed invariants and the classification follows by a deformation process or a contraction process. We focus on the case of 2- and 3-step nilpotent Lie algebras. We describe in both cases a deformation cohomology for this type of algebras and the algebras which are rigid with respect to this cohomology. Other

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