Cartan algebra

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• Cartan's criterion — is an important mathematical theorem in the foundations of Lie algebra theory that gives conditions for a Lie agebra to be nilpotent, solvable, or semisimple. It is based on the notion of the Killing form, a symmetric bilinear form on mathfrak{g} …   Wikipedia

• CARTAN (H.) — CARTAN HENRI (1904 ) Mathématicien français dont les travaux portent principalement sur les fonctions analytiques et la topologie algébrique. Fils du mathématicien Élie Cartan, Henri Cartan, né à Nancy, est un ancien élève de l’École normale… …   Encyclopédie Universelle

• Cartan —   [kar tã],    1) Élie Joseph, französischer Mathematiker, * Dolomieu (Département Isère) 9. 4. 1869, ✝ Paris 6. 5. 1951, Vater von 2); Professor in Nancy (1903 09) und Paris (1912 40); seit 1931 Mitglied der Académie des sciences. Mit dem von… …   Universal-Lexikon

• Cartan connection — In the mathematical field of differential geometry, a Cartan connection is a flexible generalization of the notion of an affine connection. It may also be regarded as a specialization of the general concept of a principal connection, in which the …   Wikipedia

• Cartan decomposition — The Cartan decomposition is a decomposition of a semisimple Lie group or Lie algebra, which plays an important role in their structure theory and representation theory. It generalizes the polar decomposition of matrices. Cartan involutions on Lie …   Wikipedia

• Cartan subalgebra — In mathematics, a Cartan subalgebra is a nilpotent subalgebra mathfrak{h} of a Lie algebra mathfrak{g} that is self normalising (if [X,Y] in mathfrak{h} for all X in mathfrak{h}, then Y in mathfrak{h}).Cartan subalgebras exist for finite… …   Wikipedia

• Cartan matrix — In mathematics, the term Cartan matrix has two meanings. Both of these are named after the French mathematician Élie Cartan. In an example of Stigler s law of eponymy, Cartan matrices in the context of Lie algebras were first investigated by… …   Wikipedia

• Cartan, Henri — ▪ 2009 Henri Paul Cartan        French mathematician born July 8, 1904, Nancy, France died Aug. 13, 2008, Paris, France made fundamental advances in the theory of analytic functions. Cartan was also a founding member of the secretive group of… …   Universalium

• Cartan subgroup — In mathematics, a Cartan subgroup of a Lie group or algebraic group G is one of the subgroups whose Lie algebrais a Cartan subalgebra. The dimension of a Cartan subgroup, and therefore of a Cartan subalgebra, is the rank of G .ConventionsThe… …   Wikipedia

• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• Cartan-Karlhede algorithm — One of the most fundamental problems of Riemannian geometry is this: given two Riemannian manifolds of the same dimension, how can one tell if they are locally isometric? This question was addressed by Elwin Christoffel, and completely solved by… …   Wikipedia