Modular Lie algebra

In mathematics, a modular Lie algebra is a Lie algebra over a field of positive characteristic. ^[1]

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Table of Contents

1. 8 relations: Algebraic group, Characteristic (algebra), Field (mathematics), Frobenius endomorphism, Lie algebra, Mathematics, Nathan Jacobson, Semisimple Lie algebra.

Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety.

See Modular Lie algebra and Algebraic group

Characteristic (algebra)

In mathematics, the characteristic of a ring, often denoted, is defined to be the smallest positive number of copies of the ring's multiplicative identity that will sum to the additive identity.

See Modular Lie algebra and Characteristic (algebra)

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

See Modular Lie algebra and Field (mathematics)

Frobenius endomorphism

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class that includes finite fields.

See Modular Lie algebra and Frobenius endomorphism

Lie algebra

In mathematics, a Lie algebra (pronounced) is a vector space \mathfrak g together with an operation called the Lie bracket, an alternating bilinear map \mathfrak g \times \mathfrak g \rightarrow \mathfrak g, that satisfies the Jacobi identity. Modular Lie algebra and Lie algebra are Lie algebras.

See Modular Lie algebra and Lie algebra

Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Modular Lie algebra and Mathematics

Nathan Jacobson

Nathan Jacobson (October 5, 1910 – December 5, 1999) was an American mathematician.

See Modular Lie algebra and Nathan Jacobson

Semisimple Lie algebra

In mathematics, a Lie algebra is semisimple if it is a direct sum of simple Lie algebras.

See Modular Lie algebra and Semisimple Lie algebra

References

[1] https://en.wikipedia.org/wiki/Modular_Lie_algebra

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