On the “Bruhat graph” of a Coxeter system
Matthew Dyer (1991)
Compositio Mathematica
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Matthew Dyer (1991)
Compositio Mathematica
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du Cloux, Fokko (2002)
Experimental Mathematics
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Jun Morita, Eugene Plotkin (2001)
Rendiconti del Seminario Matematico della Università di Padova
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Peter Slodowy (1985)
Compositio Mathematica
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M. J. Dyer (1993)
Compositio Mathematica
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Elduque, Alberto, Kochetov, Mikhail (2012)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: Primary 17B70, secondary 17B40, 16W50. Given a grading Γ : L ⨁ = g ∈ G L g on a nonassociative algebra L by an abelian group G, we have two subgroups of Aut(L): the automorphisms that stabilize each component L g (as a subspace) and the automorphisms that permute the components. By the Weyl group of Γ we mean the quotient of the latter subgroup by the former. In the case of a Cartan decomposition of a semisimple complex Lie algebra,...
De Mari, Filippo (1996)
Journal of Lie Theory
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Moszkowski, Paul (1994)
Séminaire Lotharingien de Combinatoire [electronic only]
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Daniel Beltiţă, Karl-Hermann Neeb (2008)
Studia Mathematica
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We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion...