Malcev algebras

Sagle, Arthur A.

doi:10.1090/s0002-9947-1961-0143791-x

Cited by 199 publications

(85 citation statements)

References 8 publications

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“…Everywhere below we use the term "Malcev algebra" in place of the term "finite-dimensional real Malcev algebra". Malcev algebras and alternative algebras are closely associated [10][11][12]. Any nonLie simple Malcev algebra is isomorphic to the quotient algebra A (−) /R, where A is a Cayley-Dickson algebra.…”

Section: Moufang Loops and Malcev Algebrasmentioning

confidence: 99%

On a construction of self-dual gauge fields in seven dimensions

Loginov¹,

Grishkov²

2007

JNMP

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Section: Moufang Loops and Malcev Algebrasmentioning

confidence: 99%

On a construction of self-dual gauge fields in seven dimensions

Loginov¹,

Grishkov²

2007

JNMP

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“…, y] is the Jacobian of x, y and z [8], [9], [10]. Since for a Lie algebra the Jacobian of any three elements vanishes, Lie algebras fall into the variety of Malcev algebras.…”

Section: Basic Definitions and Known Resultsmentioning

confidence: 99%

The Malcev Poisson Superalgebra of the Free Malcev Superalgebra on One Odd Generator

Shestakov¹,

Zhukavets²

2006

J. Algebra Appl.

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“…This algebra was brought in sight in [15], where it was identified as Mal'tsev's. In [16], it was proved that over a field of characteristic not 2, every four-dimensional non-Lie Mal'tsev algebra is isomorphic to M (4).…”

Section: Consider a Four-dimensional Algebra M (4) With Basis {X U mentioning

confidence: 99%

The Chevalley and Costant theorems for Mal’tsev algebras

Zhelyabin

Shestakov

2007

Algebra Logic

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Centers of universal envelopes for Mal'tsev algebras are explored. It is proved that the center of the universal envelope for a finite-dimensional semisimple Mal'tsev algebra over a field of characteristic 0 is a ring of polynomials in a finite number of variables equal to the dimension of its Cartan subalgebra, and that universal enveloping algebra is a free module over its center. Centers of universal enveloping algebras are computed for some Mal'tsev algebras of small dimensions.

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Malcev algebras

Cited by 199 publications

References 8 publications

On a construction of self-dual gauge fields in seven dimensions

On a construction of self-dual gauge fields in seven dimensions

The Malcev Poisson Superalgebra of the Free Malcev Superalgebra on One Odd Generator

The Chevalley and Costant theorems for Mal’tsev algebras

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