Lie Algebras of CL Type

ABSTRACT. Lately we observe: (1) an upsurge of interest (in particular, triggered by a paper by Atiyah and Witten) to manifolds with G(2)-type structure; (2) classifications are obtained of simple (finite dimensional and graded vectorial) Lie superalgebras over fields of complex and real numbers and of simple finite dimensional Lie algebras over algebraically closed fields of characteristic p greater than 3; (3) importance of nonintegrable distributions in observations (1) and (2).We add to interrelation of (1)- (3) an explicit description of several exceptional simple Lie algebras for p=2, 3 (Brown, Ermolaev, Frank, and Skryabin algebras, and analogs of Melikyan algebras) as subalgebras of Lie algebras of vector fields preserving nonintegrable distributions analogous to (or identical with) those preserved by g (2), o(7), sp(4), sp(10) and the Brown algebra br(3). The description is performed in terms of Cartan-Tanaka-Shchepochkina prolongs and is similar to descriptions of simple Lie superalgebras of vector fields with polynomial coefficients. Our results illustrate usefulness of Shchepochkina's algorithm and SuperLie package; at least two families of simple Lie algebras found in the process are new.

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Integrable cocycles and global deformations of Lie algebra of typeG₂in characteristic 2

Chebochko

Кузнецов

2016

Communications in Algebra

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Lie Algebras of CL Type

Cited by 3 publications

References 19 publications

Simple 14-Dimensional Lie Algebras in Characteristic Two

Simple 14-Dimensional Lie Algebras in Characteristic Two

Structures of G(2) Type and Nonintegrable Distributions in Characteristic p

Integrable cocycles and global deformations of Lie algebra of typeG₂in characteristic 2

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Lie Algebras of CL Type

Cited by 3 publications

References 19 publications

Simple 14-Dimensional Lie Algebras in Characteristic Two

Simple 14-Dimensional Lie Algebras in Characteristic Two

Structures of G(2) Type and Nonintegrable Distributions in Characteristic p

Integrable cocycles and global deformations of Lie algebra of typeG2in characteristic 2

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Integrable cocycles and global deformations of Lie algebra of typeG₂in characteristic 2