In algebra, Freudenthal algebras are certain Jordan algebras constructed from composition algebras. Suppose that C is a composition algebra over a field...

Hans Freudenthal (17 September 1905 – 13 October 1990) was a Jewish German-born Dutch mathematician. He made substantial contributions to algebraic topology...

subgroup of O(E) so a compact Lie group. Its Lie algebra consists of skew-adjoint derivations. Freudenthal (1951) showed that given X in E there is an automorphism...

examples, the structure algebra of H(A,σ) is A. Derivation and structure algebras also form part of Tits' construction of the Freudenthal magic square. A (possibly...

algebra Differential graded Lie algebra Exterior algebra F-algebra Filtered algebra Flexible algebra Freudenthal algebra Functional-theoretic algebra...

In mathematics, the Freudenthal magic square (or Freudenthal–Tits magic square) is a construction relating several Lie algebras (and their associated...

Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants...

Allen (2002), Algebraic Topology, Cambridge: Cambridge University Press, ISBN 0-521-79540-0. Whitehead, G. W. (1953), "On the Freudenthal Theorems", Annals...

others.: 463–81  Freudenthal magic square Pfister form Triality Wikibooks has a book on the topic of: Associative Composition Algebra Springer, T. A.;...

Manivel, Laurent (2001), "The projective geometry of Freudenthal's magic square", Journal of Algebra, 239 (2): 477–512, arXiv:math/9908039, doi:10.1006/jabr...

Category of Eilenberg–Moore algebras Kleisli category Adjunction (field theory) Lindenbaum–Tarski algebra construction Freudenthal magic square Stone–Čech...

construction known as the magic square, due to Hans Freudenthal and Jacques Tits. The algebraic double cover of the complex form, or of the split real...

pp. 141–189. doi:10.1007/978-3-662-03130-8_6. ISBN 978-3-540-59251-8. Freudenthal, H; van der Waerden, B. L. (1947), "Over een bewering van Euclides ("On...

systematically using a construction known as the magic square, due to Hans Freudenthal and Jacques Tits. There are 3 real forms: a compact one, a split one...

Division Algebras: Octonions, Quaternions, Complex Numbers and the Algebraic Design of Physics, Kluvwer Academic Publishers, ISBN 0-7923-2890-6 Freudenthal, Hans...

(PDF). Notices of the American Mathematical Society. 44 (3): 313–320. Freudenthal, H., 1962, "Review: B. L. van der Waerden, Science Awakening" in Bull...

Cauchy had a great influence over his contemporaries and successors; Hans Freudenthal stated: "More concepts and theorems have been named for Cauchy than for...

for the character of an irreducible representation of a semisimple Lie algebra. In Weyl's approach to the representation theory of connected compact Lie...

Eilenberg–Zilber theorem (algebraic topology) Euler's polyhedron theorem (polyhedra) Excision theorem (homology theory) Freudenthal suspension theorem (homotopy...

are part of the Freudenthal magic square. By means of a Chevalley basis for the Lie algebra, one can define E6 as a linear algebraic group over the integers...

abstract algebra, homological algebra, algebraic topology and algebraic number theory, as well as in applications to group theory proper. As in algebraic topology...

previously defined". As Freudenthal notes: 199  ...up to Hilbert, there is no other example for such a direct derivation of the algebraic laws from geometric...

using the Freudenthal diagonalization theorem due to Freudenthal (1951): he proved that given any matrix in the algebra Hr(A) there is an algebra automorphism...

C ^ 2 {\displaystyle {\hat {C}}_{2}} ⁠, 10/9. More generally, from Freudenthal's formula, for generic D(p,q), the eigenvalue of ⁠ C ^ 1 {\displaystyle...

representation of a semisimple Lie algebra. An alternative formula, that is more computationally efficient in some cases, is Freudenthal's formula. The Kostant partition...

topology Paul Epstein, number theory Adolf Fraenkel, set theory Hans Freudenthal, algebraic topology Friedrich Hartogs, mathematician Felix Hausdorff, topology...

equations. He also made substantial contributions to the development of algebra. Marius Sophus Lie was born on 17 December 1842 in the small town of Nordfjordeid...

glossary of properties and concepts in algebraic topology in mathematics. See also: glossary of topology, list of algebraic topology topics, glossary of category...

theorem on exchangeable sequences of random variables. Hans Freudenthal proves the Freudenthal suspension theorem in homotopy. Goldberg polyhedron first...

Novák 1984, p. 330. Roll 1993, p. 469; Freudenthal & Bauer 1974, p. 10 Freudenthal 1973, p. 475; Freudenthal & Bauer 1974, p. 10 Świerczkowski 1959a...