For the Lie algebras or groups, see Malcev Lie algebra.
In mathematics, a Malcev algebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that
and satisfies the Malcev identity
They were first defined by Anatoly Maltsev (1955).
Malcev algebras play a role in the theory of Moufang loops that generalizes the role of Lie algebras in the theory of groups. Namely, just as the tangent space of the identity element of a Lie group forms a Lie algebra, the tangent space of the identity of a smooth Moufang loop forms a Malcev algebra. Moreover, just as a Lie group can be recovered from its Lie algebra under certain supplementary conditions, a smooth Moufang loop can be recovered from its Malcev algebra if certain supplementary conditions hold. For example, this is true for a connected, simply connected real-analytic Moufang loop.[1]
^Nagy, Peter T. (1992). "Moufang loops and Malcev algebras" (PDF). Seminar Sophus Lie. 3: 65–68. CiteSeerX 10.1.1.231.8888.
In mathematics, a Malcevalgebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that x...
In mathematics, a Malcev Lie algebra, or Mal'tsev Lie algebra, is a generalization of a rational nilpotent Lie algebra, and Malcev groups are similar....
loops have an associated algebra, the Malcevalgebra, similar in some ways to how a Lie group has an associated Lie algebra. A Moufang loop is a loop...
been generalized for Malcevalgebras, Bol algebras and left alternative algebras.[citation needed] The universal enveloping algebra, or rather the universal...
decidability of various algebraic groups. Malcevalgebras (generalisations of Lie algebras), as well as Malcev Lie algebras are named after him. At school...
Algebra i Logika (English: Algebra and Logic) is a peer-reviewed Russian mathematical journal founded in 1962 by Anatoly Ivanovich Malcev, published by...
decidability of various algebraic groups, developed the Malcevalgebra Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford...
finite-dimensional Lie algebras and Lie groups to separate problems about Lie algebras in these two special classes, solvable and semisimple. Moreover, Malcev (1942)...
not a Lie algebra. Malcevalgebra Alternative algebra Commutant-associative algebra A. Elduque, H. C. Myung Mutations of alternative algebras, Kluwer Academic...
Jordan algebra under the product a ∘ b = ab + ba. Malcev-admissible algebra Lie-admissible algebra Okubo 1995, pp. 19, 84 Albert, A. Adrian (1948), "Power-associative...
decidability of various algebraic groups, developed the Malcevalgebra Yuri Manin, author of the Gauss–Manin connection in algebraic geometry, Manin-Mumford...
shown that Engel's theorem still holds for Leibniz algebras and that a weaker version of Levi-Malcev theorem also holds. The tensor module, T(V) , of any...
Peresi, Luiz A. (1 April 2006), "Ternary analogues of Lie and Malcevalgebras", Linear Algebra and Its Applications, 414 (1): 1–18, doi:10.1016/j.laa.2005...
Oxford University Press. p. 12. ISBN 978-0-19-853577-5. A. Malcev, On the Immersion of an Algebraic Ring into a Field, Mathematische Annalen 1937, Volume 113...
In mathematics, the structure constants or structure coefficients of an algebra over a field are the coefficients of the basis expansion (into linear combination...
1998) was a Japanese mathematician who is known for his influence on algebraic number theory. Iwasawa was born in Shinshuku-mura, a town near Kiryū,...
received an Ural Mathematical Society Award in 1984 for the solution of the Malcev–Kargapolov problem posed in 1965 about the algorithmic decidability of the...
Lie Algebras III: Structure of Lie Groups and Lie Algebras, Encyclopaedia of Mathematical Sciences, vol. 41, Springer, ISBN 9783540546832 Malcev, A. (1945)...
Google Books "p-solvable-groups". Group props wiki. Malcev, A. I. (1949), "Generalized nilpotent algebras and their associated groups", Mat. Sbornik, New...
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