Moufang Loop
Moufang is the family name of the following people: *Christoph Moufang (1817–1890), a Roman Catholic cleric *Ruth Moufang (1905–1977), a German mathematician, after whom several concepts in mathematics are named: ** Moufang–Lie algebra ** Moufang loop ** Moufang polygon ** Moufang plane *David Moufang David Moufang (born 1966, in Heidelberg, West Germany) is a German ambient techno musician. He records with his partner, Jonas Grossmann as Deep Space Network project and his solo releases as Move D.Profileat Allmusic guide His other projects inc ...

Christoph Moufang
Franz Christoph Ignaz Moufang (17 February 1817 – 27 February 1890) was a German Catholic theologian and diocesan administrator. Life Education Moufang was born at Mainz, where he also received his primary education. In 1834 he entered the Rhenish Frederick William's University of Bonn, first taking up medicine, but soon turning to theology. Among his masters were Klee, Windischmann, and Walter. In 1837 he went to Munich, and then next year took the prescribed theological examinations at Gießen, after which he entered the ecclesiastical seminary at Mainz, where he was ordained to the priesthood on 19 December 1839. His first appointment was as curate in Seligenstadt, where his uncle, Adam Franz Lennig, later vicar-general and dean of the Mainz Cathedral, was pastor. Lennig stimulated in him a broad interest for the religious questions of the time. Moufang also taught at the pro-gymnasium at Seligenstadt. After Seligenstadt he was charged with the parish of Bensheim, then ...
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Ruth Moufang
Ruth Moufang (10 January 1905 Р26 November 1977) was a German mathematician. Biography Born to German chemist Eduard Moufang and Else Fecht Moufang. Eduard Moufang was the son of Friedrich Carl Moufang (1848-1885) from Mainz, and Elisabeth von Moers from Mainz. Ruth Moufang's mother was Else Fecht, who was the daughter of Alexander Fecht (1848-1913) from Kehl and Ella Scholtz (1847-1921). Ruth was the younger of her parents' two daughters, having an elder sister named Erica. Education and career She studied mathematics at the University of Frankfurt. In 1931 she received her Ph.D. on projective geometry under the direction of Max Dehn, and in 1932 spent a fellowship year in Rome. After her year in Rome, she returned to Germany to lecture at the University of K̦nigsberg and the University of Frankfurt. Denied permission to teach by the minister of education of Nazi Germany, she worked in private industry at the Krupps Research Institute, where she became the first Germ ...
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Moufang–Lie Algebra
In mathematics, a Malcev algebra (or Maltsev algebra or Moufang–Lie algebra) over a field is a nonassociative algebra that is antisymmetric, so that :xy = -yx and satisfies the Malcev identity :(xy)(xz) = ((xy)z)x + ((yz)x)x + ((zx)x)y. They were first defined by Anatoly Maltsev (1955). Malcev algebras play a role in the theory of Moufang loops that generalizes the role of Lie algebras in the theory of groups. Namely, just as the tangent space of the identity element of a Lie group forms a Lie algebra, the tangent space of the identity of a smooth Moufang loop forms a Malcev algebra. Moreover, just as a Lie group can be recovered from its Lie algebra under certain supplementary conditions, a smooth Moufang loop can be recovered from its Malcev algebra if certain supplementary conditions hold. For example, this is true for a connected, simply connected real-analytic Moufang loop. Examples *Any Lie algebra is a Malcev algebra. *Any alternative algebra may be made into a Mal ...
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Moufang Loop
Moufang is the family name of the following people: *Christoph Moufang (1817–1890), a Roman Catholic cleric *Ruth Moufang (1905–1977), a German mathematician, after whom several concepts in mathematics are named: ** Moufang–Lie algebra ** Moufang loop ** Moufang polygon ** Moufang plane *David Moufang David Moufang (born 1966, in Heidelberg, West Germany) is a German ambient techno musician. He records with his partner, Jonas Grossmann as Deep Space Network project and his solo releases as Move D.Profileat Allmusic guide His other projects inc ...

Moufang Polygon
In mathematics, Moufang polygons are a generalization by Jacques Tits of the Moufang planes studied by Ruth Moufang, and are irreducible buildings of rank two that admit the action of root groups. In a book on the topic, Tits and Richard Weiss classify them all. An earlier theorem, proved independently by Tits and Weiss, showed that a Moufang polygon must be a generalized 3-gon, 4-gon, 6-gon, or 8-gon, so the purpose of the aforementioned book was to analyze these four cases. Definitions *A generalized ''n''-gon is a bipartite graph of diameter ''n'' and girth 2''n''. *A graph is called thick if all vertices have valence at least 3. *A root of a generalized ''n''-gon is a path of length ''n''. *An apartment of a generalized ''n''-gon is a cycle of length 2''n''. *The root subgroup of a root is the subgroup of automorphisms of a graph that fix all vertices adjacent to one of the inner vertices of the root. *A Moufang ''n''-gon is a thick generalized ''n''-gon (with ''n''>2) such th ...
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Moufang Plane
In geometry, a Moufang plane, named for Ruth Moufang, is a type of projective plane, more specifically a special type of translation plane. A translation plane is a projective plane that has a ''translation line'', that is, a line with the property that the group of automorphisms that fixes every point of the line acts transitively on the points of the plane not on the line. A translation plane is Moufang if every line of the plane is a translation line. Characterizations A Moufang plane can also be described as a projective plane in which the '' little Desargues theorem'' holds. This theorem states that a restricted form of Desargues' theorem holds for every line in the plane. For example, every Desarguesian plane is a Moufang plane. In algebraic terms, a projective plane over any alternative division ring is a Moufang plane, and this gives a 1:1 correspondence between isomorphism classes of alternative division rings and Moufang planes. As a consequence of the algebraic Artinâ ...
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