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Topic: Cartan subalgebra

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Cartan connection

lie Cartan

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Cartan subalgebra

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	General Algebraic - General Algebraic
		For example, for the algebras of n by n matrices of trace zero, the bilinear form is (a, b) = Trace(ab), the Cartan involution is given by minus the transpose, and the grading can be given by "distance from the diagonal" so that the Cartan subalgebra is the diagonal elements.
		A generalized Kac-Moody algebra is obtained from a universal one by changing the Cartan matrix, by the operations of killing something in the center, or taking a central extension, or adding outer derivations.
		Algebras with Lorentzian Cartan subalgebra whose denominator function is an automorphic form of singular weight.
	www.infotechloco.com /Inf-Programming-F---L/General-Algebraic.html (741 words)

	Cartan Subalgebras And Bimodule Decompositions Of II1 Factors (ResearchIndex) (Site not responding. Last check: 2007-09-30)
		Cartan Subalgebras And Bimodule Decompositions Of II1 Factors (2000)
		Let A # M be a MASA in a II 1 factor M. We describe the von Neumann subalgebra of M generated by A and its normalizer N (A) as the set N w q (A) consisting of those elements m # M for which the bimodule AmA is discrete.
		As a consequence, we show that A is a Cartan subalgebra of M iff for any MASA B #M, B = uAu #...
	citeseer.ist.psu.edu /380284.html (342 words)

	Root Systems (Site not responding. Last check: 2007-09-30)
		A sequence R giving the set of roots of L with respect to the Cartan subalgebra which is output by
		The Cartan matrix of the sequence of fundamental roots.
		The first sequence gives basis elements corresponding to positive roots, the second to the negative roots and the third to basis elements in a Cartan subalgebra.
	www.umich.edu /~gpcc/scs/magma/text947.htm (261 words)

	NSDL Metadata Record -- Borel subalgebra
		a Cartan subalgebra, R the associated root system, and...
		We have a root decomposition into the Cartan subalgebra and the root spaces...
		be the direct sum of the Cartan subalgebra and the positive root spaces.
	nsdl.org /mr/1031979 (43 words)

	Citations: Computing the structure of a Lie algebra - Beck, Kolman, Stewart (ResearchIndex)
		A Levi subalgebra of L is a semisimple subalgebra S such that L = RoS.
		In the first part of the algorithm a series of subalgebras 0 ae K 1 ae K 2 ae Delta Delta Delta ae K r Gamma1 = R is constructed such that K....
		) lower and upper central series (1] a Cartan subalgebra (1] 21] 13] a Levi subalgebra (18] 12] the solvable radical (1] the nilradical (1] 18] 19] Table 1: Material invariants of Lie algebras By calculating numerical invariants of the Lie algebras L 1 and L 2 we may be.
	citeseer.ist.psu.edu /context/1028441/0 (933 words)

	[No title] (Site not responding. Last check: 2007-09-30)
		D It is called Cartan subalgebra and denoted h.
		This decomposition is called Cartan decomposition, and h is the Cartan subalgebra.
		It is also a representation of its Cartan subalgebra h.
	knaan.com /Lev/Seminar/IntLieAlgSrucTheo.doc (573 words)

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