In mathematics, the Iwasawa decomposition (aka KAN from its expression) of a semisimple Lie group generalises the way a square real matrix can be written...

Iwasawa may refer to: Kenkichi Iwasawa (岩澤 健吉, 1917–1998), Japanese mathematician Iwasawa decomposition, a mathematical group decomposition Iwasawa group...

the general Iwasawa decomposition. Lectures on p-adic L-functions / by Kenkichi Iwasawa (1972) Local class field theory / Kenkichi Iwasawa (1986) ISBN 0-19-504030-9...

where B = J. The Iwasawa decomposition G C = G ⋅ A ⋅ N {\displaystyle \displaystyle {G_{\mathbf {C} }=G\cdot A\cdot N}} gives a decomposition for GC for which...

Gram and Schmidt. In the theory of Lie group decompositions, it is generalized by the Iwasawa decomposition. The application of the Gram–Schmidt process...

In linear algebra, a QR decomposition, also known as a QR factorization or QU factorization, is a decomposition of a matrix A into a product A = QR of...

Jordan–Chevalley decomposition also exist for elements of Linear algebraic groups and Lie groups via a multiplicative reformulation. The decomposition is an important...

greater than 2 there is one conjugacy class for a given trace. The Iwasawa decomposition of a group is a method to construct the group as a product of three...

semidirect product with A normalizing N. Moreover, G has the following Iwasawa decomposition: G = K A N . {\displaystyle \displaystyle {G=KAN.}} For i ≠ j let...

Jordan–Chevalley decomposition of an element in algebraic group as a product of semisimple and unipotent elements The Bruhat decomposition G = BWB of a semisimple...

Lie group with Iwasawa decomposition G=NAK g is an element of G ρ is a Weyl vector a(g) is the element a in the Iwasawa decomposition g=nak Harish-Chandra...

Brian Finnegan and Aidan O'Rourke kan, PDP ligand, kanamycin A Iwasawa decomposition of a Lie group in mathematics A Japanese unit of mass (貫) Kan, a...

the restricted root system and its Weyl group are related to the Iwasawa decomposition of the Lie group. Satake diagram Bump, Daniel (2004), Lie groups...

Gram-Schmidt process. For a general semisimple Lie group, the decomposition is the Iwasawa decomposition of G as G = KAN in which K occurs in a product with a...

spherical representations. The theorem can be proved using the Iwasawa decomposition: g = k ⊕ a ⊕ n , {\displaystyle {\mathfrak {g}}={\mathfrak {k}}\oplus...

PSL2(R), which is obtained by taking the quotient by the center. By Iwasawa decomposition, both groups are circle bundles over the complex upper half-plane...

dimension splits into g and a certain solvable Lie algebra (the Iwasawa decomposition), and this provides a canonical bicrossproduct quantum group associated...

semisimple Lie group G, the subgroup H is constructed starting from the Iwasawa decomposition G = KAN with K a maximal compact subgroup. Then H is chosen to contain...

Kostant, Bertram (1973). "On convexity, the Weyl group and the Iwasawa decomposition". Annales Scientifiques de l'École Normale Supérieure. 6 (4): 413–455...

has an Iwasawa–Monod decomposition, namely G = K P for some amenable subgroup P of G. This is the abstract analogue of the Iwasawa decomposition of semisimple...

points in the boundary. The Iwasawa decomposition of P U ( n , 1 ) {\displaystyle \mathrm {PU} (n,1)} is the decomposition P U ( n , 1 ) = K × A × N {\displaystyle...

Lie group that is invariant under inner automorphisms. Iwasawa decomposition Iwasawa decomposition Jacobi identity 1.   Carl Gustav Jacob Jacobi (1804 –...

theorem Hasse norm theorem Artin reciprocity Local class field theory Iwasawa theory Herbrand–Ribet theorem Vandiver's conjecture Stickelberger's theorem...

convexity theorem concerning the projection onto the component A in the Iwasawa decomposition G = KAN of a real semisimple Lie group G. The result discussed above...

element of A* =Hom(A,T) where A is the Abelian vector subgroup in the Iwasawa decomposition G =KAN of G; λ' is defined on G by first extending λ to a character...

which can be described completely in terms of root data and a given Iwasawa decomposition. Moreover, there is a maximal such space, with quotient maps going...

Kostant, Bertram (1973), "On convexity, the Weyl group and the Iwasawa decomposition", Annales Scientifiques de l'École Normale Supérieure, Série 4,...

(1st ed.). New York: Wiley-Interscience. pp. 34–35. ISBN 9780471396987. Iwasawa, Tetsuo; Tokunaga, Makoto; Obora, Yasushi; Tsuji, Yasushi (2004-06-01)...

confirmed in 1980 by Simon P. Norton and others using computer calculations. Iwasawa group Lyons group Thin group (finite group theory) Umro Zvonimir Janko...

Michael; Dooley A. H.; Koranyi A.; Ricci F. (1991). "H-type groups and Iwasawa decompositions". Advances in Mathematics. 87 (1): 1–41. doi:10.1016/0001-8708(91)90060-K...