of Lie algebras, the Poincaré–Birkhoff–Witt theorem (or PBW theorem) is a result giving an explicit description of the universal enveloping algebra of...

representation of a semisimple Lie algebra. In Weyl's approach to the representation theory of connected compact Lie groups, the proof of the character...

multiplication operation in the Lie algebra. The close relation to SU(1,c) and SO(3,r) is evident in the isomorphism of their Lie algebras. Lie groups that contain...

In mathematics, a tensor is an algebraic object that describes a multilinear relationship between sets of algebraic objects associated with a vector space...

{\displaystyle H} is a one-dimensional Lie group central extension of G {\displaystyle G} , so that the Lie algebra h {\displaystyle {\mathfrak {h}}} of...

letter D stands for Darstellung,[citation needed] which means "representation" in German. Let Jx, Jy, Jz be generators of the Lie algebra of SU(2) and SO(3)...

History of Lie Groups and Algebraic Groups, American Mathematical Society, ISBN 978-0-8218-0288-5 Brauer, R. (1935), Über die Darstellung von Gruppen...

In abstract algebra, the symmetric group defined over any set is the group whose elements are all the bijections from the set to itself, and whose group...

this time, and certainly much helped by Weyl's expositions, Lie groups and Lie algebras became a mainstream part both of pure mathematics and theoretical...

Springer-Verlag, ISBN 978-0-387-94285-8 Schur, Issai (1904), "Über die Darstellung der endlichen Gruppen durch gebrochene lineare Substitutionen.", Journal...

his 1855 paper "Theorie der Kreisverwandtschaft in rein geometrischer Darstellung". Karl Wilhelm Feuerbach and Julius Plücker are also credited with originating...

(1964), Elements of real analysis, pp. 315–316 Weierstrass, Karl (1841). "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter...

number by another rational number is larger than the lower bound for algebraic numbers, which is itself larger than the lower bound for all real numbers...

(2 ed.), Springer, ISBN 978-0-387-94461-6 Schur, Issai (1911), "Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare...

"Theorie der automorphen Formen beliebiger reeller Dimension und ihre Darstellung durch eine neue Art Poincaréscher Reihen". Mathematische Annalen (in...

fundamentalen physikalischen Eigenschaften der Krystalle in elementarer Darstellung. Leipzig: Von Veit. Poincaré, Henri, "Analysis situs", Journal de l'École...

The Theory of Science: Die Wissenschaftslehre oder Versuch einer Neuen Darstellung der Logik. Translated by Rolf, George. University of California Press...

with his three chief mathematical works Beyträge zu einer begründeteren Darstellung der Mathematik (1810), Der binomische Lehrsatz (1816) and Rein analytischer...

1007/978-1-4419-7323-8_1, ISBN 978-1-4419-7322-1 Weierstrass, Karl (1841), "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter...

Press, ISBN 978-0-19-853556-0, MR 1205350 Schur, J. (1911), "Über die Darstellung der symmetrischen und der alternierenden Gruppe durch gebrochene lineare...

is a transcendental number, meaning that it cannot be a solution of an algebraic equation involving only finite sums, products, powers, and integers. The...

MR 0169108, Zbl 0128.15403 Fueter, Rudolf (1936), "Über die analytische Darstellung der regulären Funktionen einer Quaternionenvariablen", Commentarii Mathematici...

transformation of the Sine-Gordon equation, Biquaternion algebra, split-complex numbers, Clifford algebra, and others. Learning materials from Wikiversity: The...

trigonometric series," 1834 (Lobachevsky 1951, pp. 31–80). Über die Darstellung ganz willkürlicher Funktionen durch Sinus- und Cosinusreihen," 1837 (Dirichlet...

und Kartographie im Islam und ihr Fortleben im Abendland, Historische Darstellung, Teil 1–3 (in German), Frankfurt am Main{{citation}}: CS1 maint: location...

ISBN 978-3-406-09412-5. Endres, Rudolf (1984). Erlangen. Geschichte der Stadt in Darstellung und Bilddokumenten. Munich: Alfred Wendehorst. pp. 31, 33, 40, 41. Deuerlein...

Strand MP, Reinhardt WP (1979). "Semiclassical quantization of the low lying electronic states of H2+". Journal of Chemical Physics. 70 (8): 3812–3827...