scholarly journals DERIVATIONS OF THE ODD CONTACT LIE ALGEBRAS IN PRIME CHARACTERISTIC

2013 ◽  
Vol 50 (3) ◽  
pp. 591-605
Author(s):  
Yan Cao ◽  
Xiumei Sun ◽  
Jixia Yuan
Keyword(s):  
Lie Algebras ◽  
Prime Characteristic

On the Extensions of Lie Algebras

1968 ◽  
Vol 20 ◽  
pp. 1439-1450 ◽  
Author(s):  
Richard E. Block
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Prime Characteristic

In this paper we give some results on the extensions of Lie algebras, with emphasis on the case of prime characteristic, although part of the paper is also of interest at characteristic 0. An extension of a Lie algebra L is a pair (E, π), where £ is a Lie algebra and π is a homomorphism of E onto L. The kernel K of the extension is ker π.

scholarly journals Free Lie algebras as modules for symmetric groups

1999 ◽  
Vol 67 (2) ◽  
pp. 143-156 ◽  
Author(s):  
R. M. Bryant ◽  
L. G. Kovács ◽  
Ralph Stöhr
Keyword(s):  
Lie Algebras ◽  
Symmetric Groups ◽  
Free Lie Algebra ◽  
Prime Characteristic ◽  
Specht Modules ◽  
Generating Set ◽  
Direct Sum ◽  
Finite Dimensional ◽  
Free Lie Algebras ◽  
Direct Decompositions

AbstractLet r be a positive integer, F a field of odd prime characteristic p, and L the free Lie algebra of rank r over F. Consider L a module for the symmetric group , of all permutations of a free generating set of L. The homogeneous components Ln of L are finite dimensional submodules, and L is their direct sum. For p ≤ r ≤ 2p, the main results of this paper identify the non-porojective indecomposable direct summands of the Ln as Specht modules or dual Specht modules corresponding to certain partitions. For the case r = p, the multiplicities of these indecomposables in the direct decompositions of the Ln are also determined, as are the multiplicities of the projective indecomposables. (Corresponding results for p = 2 have been obtained elsewhere.)

scholarly journals Soluble Lie algebras having finite-dimensional maximal subalgebras

1974 ◽  
Vol 11 (1) ◽  
pp. 145-156 ◽  
Author(s):  
Ian N. Stewart
Keyword(s):  
Lie Algebras ◽  
Minimal Ideal ◽  
Prime Characteristic ◽  
Maximal Subalgebra ◽  
Maximal Subalgebras ◽  
Infinite Dimensional ◽  
The Core ◽  
Zero Characteristic ◽  
Finite Dimensional ◽  
Split Extensions

Infinite-dimensional soluble Lie algebras can possess maximal subalgebras which are finite-dimensional. We give a fairly complete description of such algebras: over a field of prime characteristic they do not exist; over a field of zero characteristic then, modulo the core of the aforesaid maximal subalgebra, they are split extensions of an abelian minimal ideal by the maximal subalgebra. If the field is algebraically closed, or if the maximal subalgebra is supersoluble, then all finite-dimensional maximal subalgebras are conjugate under the group of automorphisms generated by exponentials of inner derivations by elements of the Fitting radical. An example is given to indicate the differences encountered in the insoluble case, and the nonexistence of group-theoretic analogues is briefly discussed.

scholarly journals Algebraic approach to Rump’s results on relations between braces and pre-lie algebras

2020 ◽  
pp. 2250054
Author(s):  
Agata Smoktunowicz
Keyword(s):  
Lie Algebras ◽  
Characteristic Zero ◽  
Algebraic Approach ◽  
Geometric Approach ◽  
Prime Characteristic ◽  
Affine Manifolds ◽  
Algebraic Interpretation

In 2014, Wolfgang Rump showed that there exists a correspondence between left nilpotent right [Formula: see text]-braces and pre-Lie algebras. This correspondence, established using a geometric approach related to flat affine manifolds and affine torsors, works locally. In this paper, we explain Rump’s correspondence using only algebraic formulae. An algebraic interpretation of the correspondence works for fields of sufficiently large prime characteristic as well as for fields of characteristic zero.

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