free Lie algebra

free Lie algebra
свободная алгебра Ли

Англо-русский технический словарь.

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  • Free Lie algebra — In mathematics, a free Lie algebra, over a given field K, is a Lie algebra generated by a set X, without any imposed relations. Contents 1 Definition 2 Universal enveloping algebra 3 Hall sets …   Wikipedia

  • Affine Lie algebra — In mathematics, an affine Lie algebra is an infinite dimensional Lie algebra that is constructed in a canonical fashion out of a finite dimensional simple Lie algebra. It is a Kac–Moody algebra whose generalized Cartan matrix is positive semi… …   Wikipedia

  • Graded Lie algebra — In mathematics, a graded Lie algebra is a Lie algebra endowed with a gradation which is compatible with the Lie bracket. In other words, a graded Lie algebra is a Lie algebra which is also a nonassociative graded algebra under the bracket… …   Wikipedia

  • Malcev Lie algebra — 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. Both were introduced by Quillen (1969, Appendix A3), based on the work of (Mal cev 1949).… …   Wikipedia

  • Free group — In mathematics, a group G is called free if there is a subset S of G such that any element of G can be written in one and only one way as a product of finitely many elements of S and their inverses (disregarding trivial variations such as st 1 =… …   Wikipedia

  • Lie derivative — In mathematics, the Lie derivative, named after Sophus Lie by Władysław Ślebodziński, evaluates the change of one vector field along the flow of another vector field.The Lie derivative is a derivation on the algebra of tensor fields over a… …   Wikipedia

  • Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… …   Wikipedia

  • Free probability — is a mathematical theory which studies non commutative random variables. The freeness property is the analogue of the classical notion of independence, and it is connected with free products. This theory was initiated by Dan Voiculescu around… …   Wikipedia

  • Free Speech on Evolution — is a Discovery Institute intelligent design campaign. It began in 2005 and has been run hand in hand with the Institute s Teach the Controversy campaign. Its goal is to introduce intelligent design into United States public high school science… …   Wikipedia

  • List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this …   Wikipedia

  • Trace (linear algebra) — In linear algebra, the trace of an n by n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i.e., where aii represents the entry on the ith row and ith column …   Wikipedia


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