Lie Algebras and Lie Groups

By William Fulton, J. Harris. 2004

589 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df705e25fe9dde321798a639de0c1f67c1b4b617

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In Algebra and Number Theory

In Mathematical Physics

Citations in the corpus

Algebraic Methods in Unstable Homotopy Theory (2010, background): “The proof below is based on an argument in Serre’s book on Lie algebras [119].”
A complex ball uniformization of the moduli space of cubic surfaces via periods of K 3 surfaces (2003, background): “All of this is well-known and can be found, for example, in [Bo], Chapter 6, §4, exercise 2.”
Leibniz n-algebras (2002, unknown): “Let us recall (see [8]) that a magma M is a set together with a map (binary operation) M M!M; x; y 7! x i y:”
Control Principles of Complex Networks (2015, methodology): “This can be achieved by constructing the Philip Hall basis of the Lie algebra, which essentially follows a breadth-first search and the search depth is defined to be the number of nested levels of bracket operations (Duleba, 1998; Serre, 1992).”
Differential Geometry and Lie Groups (2020, methodology): “A more concise proof is given in Serre [105] (Chapter VI, Theorem 2.”
A finiteness theorem for the Brauer group of abelian varieties and K3 surfaces (2006, background): “Let G ,k be the image of Γ = Gal (k/k) in Aut Q (V ); it is a compact subgroup of Aut Q (V ) and, by the -adic version of Cartan’s theorem [24], is an -adic Lie subgroup of Aut Q (V ).”
Topics Surrounding the Anabelian Geometry of Hyperbolic Curves (2003, background): “By [Ser1], Chapter V, § 7, 9, after possibly replacing n by a larger n, we may assume that α is the homomorphism obtained by exponentiating A.”
The structure of approximate groups (2011, background): “16 and the discussion in Serre’s book [49]).”
Hilbert's Fifth Problem and Related Topics (2014, background): “(As noted by Serre [Se1964], though, a certain amount of this sort of difficulty in the proof may in fact be necessary, given that the global form of Lie’s third theorem is known to fail in the infinite-dimensional case.”