Results 1 
4 of
4
DEFORMATIONS OF RESTRICTED SIMPLE LIE ALGEBRAS II
, 2007
"... Abstract. We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartantype: the Contact and the Hamiltonian Lie algebras. 1. ..."
Abstract

Cited by 6 (5 self)
 Add to MetaCart
Abstract. We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartantype: the Contact and the Hamiltonian Lie algebras. 1.
INFINITESIMAL DEFORMATIONS OF SYMMETRIC SIMPLE MODULAR LIE ALGEBRAS AND LIE SUPERALGEBRAS
, 807
"... Abstract. Over algebraically closed fields of positive characteristic, infinitesimal deformations of simple finite dimensional symmetric (the ones that with every root have its opposite of the same multiplicity) Lie algebras and Lie superalgebras are described for small ranks. The results are obtain ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. Over algebraically closed fields of positive characteristic, infinitesimal deformations of simple finite dimensional symmetric (the ones that with every root have its opposite of the same multiplicity) Lie algebras and Lie superalgebras are described for small ranks. The results are obtained by means of the Mathematica based code SuperLie. The infinitesimal deformation given by any odd cocycle is integrable. The moduli of the deformations form, in general, a supervariety. Not each even cocycle is integrable; but for those that are integrable, the global deforms (the results of deformations) are linear with respect to the parameter. In characteristic 2, the simple 3dimensional Lie algebra admits a parametric family of nonisomorphic simple deforms. Some of Shen’s ”variations of G(2) theme ” are interpreted as two global deforms corresponding to the several of the 20 infinitesimal deforms first found by Chebochko; we give their explicit form. 1.
DEFORMATIONS OF THE LIE ALGEBRA o(5) IN CHARACTERISTICS 3 AND 2
, 909
"... Abstract. The finite dimensional simple modular Lie algebras with Cartan matrix cannot be deformed if the characteristic p of the ground field is equal to 0 or greater than 3. If p = 3, the orthogonal Lie algebra o(5) is one of the two simple modular Lie algebras with Cartan matrix that have deforma ..."
Abstract
 Add to MetaCart
Abstract. The finite dimensional simple modular Lie algebras with Cartan matrix cannot be deformed if the characteristic p of the ground field is equal to 0 or greater than 3. If p = 3, the orthogonal Lie algebra o(5) is one of the two simple modular Lie algebras with Cartan matrix that have deformations (the Brown algebras br(2; α) are among these 10dimensional deforms and hence are not counted separately); the 29dimensional Brown algebra br(3) is the only other simple Lie algebra with Cartan matrix that has deformations. Kostrikin and Kuznetsov described the orbits (isomorphism classes) under the action of the group O(5) of automorphisms of o(5) on the space H 2 (o(5); o(5)) and produced representatives of the isomorphism classes. Here we explicitly describe global deforms of o(5) and of the simple analog of this orthogonal Lie algebra in characteristic 2. 1.
Simple finite group schemes and their infinitesimal deformations
, 811
"... We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these two simple objects have been classified. We review this classi ..."
Abstract
 Add to MetaCart
We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these two simple objects have been classified. We review this classification. Finally, we address the problem of determining the infinitesimal deformations of simple finite group schemes.