Mathematics simple lie group (11 Ergebnisse)

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Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, a simple Lie group is a connected non-abelian Lie group G which does not have nontrivial connected normal subgroups. A simple Lie algebra is a non-abelian Lie algebra whose only ideals are 0 and itself. A direct sum of simple Lie algebras is called a semisimple Lie algebra. An equivalent definition of a simple Lie group follows from the Lie correspondence: a connected Lie group is simple if its Lie algebra is simple. An important technical point is that a simple Lie group may contain discrete normal subgroups, hence being a simple Lie group is different from being simple as an abstract group. Simple Lie groups include many classical Lie groups, which provide a group-theoretic underpinning for spherical geometry, projective geometry and related geometries in the sense of Felix Klein''s Erlangen programme. It emerged in the course of classification of simple Lie groups that there exist also several exceptional possibilities not corresponding to any familiar geometry. These exceptional groups account for many special examples and configurations in other branches of mathematics, as well as contemporary theoretical physics.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In theoretical physics and mathematics, the Wess Zumino Witten (WZW) model, also called the Wess Zumino Novikov Witten model, is a simple model of conformal field theory whose solutions are realized by affine Kac Moody algebras. It is named after Julius Wess, Bruno Zumino, Sergei P. Novikov and Edward Witten. Let G denote a compact simply-connected Lie group and g its simple Lie algebra. Suppose that is a G-valued field on the complex plane. More precisely, we want to be defined on the Riemann sphere S2, which is the complex plane compactified by adding a point at infinity.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights. It is named after Hermann Weyl, who proved it in the late 1920s. By definition, the character of a representation r of G is the trace of r(g), as a function of a group element g in G. The irreducible representations in this case are all finite-dimensional (this is part of the Peter-Weyl theorem); so the notion of trace is the usual one from linear algebra. Knowledge of the character of r is a good substitute for r itself, and can have algorithmic content. Weyl's formula is a closed formula for the , in terms of other objects constructed from G and its Lie algebra. The representations in question here are complex, and so without loss of generality are unitary representations; irreducible therefore means the same as indecomposable, i.e. not a direct sum of two subrepresentations.…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - High Quality Content by WIKIPEDIA articles! In mathematics, the name symplectic group can refer to two different, but closely related, types of mathematical groups. In this article, we shall denote these two groups Sp(2n, F) and Sp(n). The latter is sometimes called the compact symplectic group to distinguish it from the former. Note that many authors prefer slightly different notations, usually differing by factors of 2. The notation used here is consistent with the size of the matrices used to represent the groups. In Cartan's classification of the simple Lie algebras, the Lie algebra of the complex group Sp(2n, C) is denoted Cn, and Sp(n) is the compact real form of Sp(2n, C).…

Taschenbuch. Zustand: Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, E8 is the name given to several closely related exceptional simple Lie groups and Lie algebras of dimension 248; the same notation is sometimes used for their root lattice, which has rank 8. Wilhelm Killing discovered the complex Lie algebra E8 during his classification of simple compact Lie algebras, though he did not prove its existence, which was first shown by Élie Cartan. Cartan also classified the three real forms of the Lie algebra, which correspond to 5 different real Lie groups of dimension 248, one of which is compact. There are also forms of the E8 groups and Lie algebras over other fields; for example, the E8 groups over finite fields form one of the infinite series of finite simple groups. The designation E8 comes from Killing and Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled An, Bn, Cn, Dn, and five exceptional cases labeled E6, E7, E8, F4, and G2. The E8 algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.…

Taschenbuch. Zustand: Neu. E8 (Mathematics) | Mathematics, Simple Lie group, Root system, Cartan subgroup, Wilhelm Killing, Élie Cartan | Frederic P. Miller (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786131755392 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Zustand: Neu. Wess-Zumino-Witten Model | Theoretical Physics, Mathematics, Conformal Field Theory, Affine Lie Algebra, Lie Group, Simply Connected Space, Simple Lie Group, Complex Plane, Point at Infinity | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130365479 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Zustand: Neu. Weyl Character Formula | Mathematics, Representation Theory, Compact Group, Weight (representation theory), Hermann Weyl, Unitary Representation, Lie Algebra, Simple Module, Ring Theory | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130366186 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…

Taschenbuch. Zustand: Neu. Simple Lie Group | Mathematics, Normal Subgroups, Connected Space, Semisimple Lie algebra | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130579920 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand. …

Taschenbuch. Zustand: Neu. Symplectic Group | Group (mathematics), Simple Lie Group, Symplectic Matrix, Matrix Multiplication, Special Linear Group, Linear Map, Degenerate Form, Simply Connected Space, Fundamental Group | Lambert M. Surhone (u. a.) | Taschenbuch | Englisch | 2026 | OmniScriptum | EAN 9786130358099 | Verantwortliche Person für die EU: preigu GmbH & Co. KG, Lengericher Landstr. 19, 49078 Osnabrück, mail[at]preigu[dot]de | Anbieter: preigu Print on Demand.…