On the first cohomology of an algebraic group and its Lie algebra in positive characteristic

Ibraev, Sh. Sh.

doi:10.1134/s0001434614090247

Cited by 4 publications

(2 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The results of Ibraev [34,35] and Permyakov [52] imply a complete description of central extensions and derivations of simple Lie algebras of "classical type" (i.e., of the form g(A) or g(A) (i) /c, except for wk and br cases) for p > 0. Therefore, we will not consider these cases, except for an occasional illustration (but we do consider wk and br cases-new results).…”

Section: Proofmentioning

confidence: 99%

See 1 more Smart Citation

Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras

Bouarroudj¹,

Grozman²,

Lebedev³

et al. 2023

SIGMA

View full text Add to dashboard Cite

Over algebraically closed fields of positive characteristic, for simple Lie (super)algebras, and certain Lie (super)algebras close to simple ones, with symmetric root systems (such that for each root, there is minus it of the same multiplicity) and of ranks less than or equal to 8—most needed in an approach to the classification of simple vectorial Lie superalgebras (i.e., Lie superalgebras realized by means of vector fields on a supermanifold),—we list the outer derivations and nontrivial central extensions. When the conjectural answer is clear for the infinite series, it is given for any rank. We also list the outer derivations and nontrivial central extensions of one series of non-symmetric (except when considered in characteristic 2), namely periplectic, Lie superalgebras—the one that preserves the nondegenerate symmetric odd bilinear form, and of the Lie algebras obtained from them by desuperization. We also list the outer derivations and nontrivial central extensions of an analog of the rank 2 exceptional Lie algebra discovered by Shen Guangyu. Several results indigenous to positive characteristic are of particular interest being unlike known theorems for characteristic 0, some results are, moreover, counterintuitive.

show abstract

Section: Proofmentioning

confidence: 99%

“…(b1) See [27,34,35]. For g = psl(3), for a basis of H 1 (g; g) we can take the following 7 derivations (recall convention (1.1))…”

Section: )mentioning

confidence: 99%

Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras

Bouarroudj¹,

Grozman²,

Lebedev³

et al. 2023

SIGMA

View full text Add to dashboard Cite

show abstract

Double Extensions of Restricted Lie (Super)Algebras

2020

View full text Add to dashboard Cite

On Cohomology of Simple Modules for Modular Classical Lie Algebras

Ibraev

Kainbaeva

Menlikozhaeva

2022

Axioms

View full text Add to dashboard Cite

In this article, we obtain some cohomology of classical Lie algebras over an algebraically closed field of characteristic p > h, where h is a Coxeter number, with coefficients in simple modules. We assume that these classical Lie algebras are Lie algebras of semisimple and simply connected algebraic groups. To describe the cohomology of simple modules, we will use the properties of the connections between ordinary and restricted cohomology of restricted Lie algebras.

show abstract

On the first cohomology of an algebraic group and its Lie algebra in positive characteristic

Cited by 4 publications

References 11 publications

Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras

Derivations and Central Extensions of Symmetric Modular Lie Algebras and Superalgebras

Double Extensions of Restricted Lie (Super)Algebras

On Cohomology of Simple Modules for Modular Classical Lie Algebras

Contact Info

Product

Resources

About