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4 days ago · Algebra and number theory. Poincaré introduced group theory to physics, and was the first to study the group of Lorentz transformations. He also made major contributions to the theory of discrete groups and their representations.
May 23, 2024 · In these theories the Poincaré algebra is replaced by a supersymmetry algebra which is a Z 2-graded Lie algebra extending the Poincaré algebra. The structure of such an algebra is to a large degree fixed by the demands of Lorentz invariance.
May 16, 2024 · William L. Hosch. Henri Poincaré was a French mathematician, one of the greatest mathematicians and mathematical physicists at the end of 19th century. He made a series of profound innovations in geometry, the theory of differential equations, electromagnetism, topology, and the philosophy of mathematics. Poincaré.
May 7, 2024 · In dimensional d = 3, 4, 6, 10. d = 3, 4, 6, 10. , 𝔰𝔦𝔰𝔬(d − 1, 1) siso ( d − 1, 1) has a nontrivial 3-cocycle given by. (ψ, ϕ, A) ↦ g(ψ ⋅ ϕ, A) ( ψ, ϕ, A) ↦ g ( ψ ⋅ ϕ, A) for spinors ψ, ϕ ∈ and vectors A ∈ 𝒯, and 0 otherwise. In dimensional d = 4, 5, 7, 11, 𝔰𝔦𝔰𝔬(d − 1, 1) has a nontrivial 4 ...
May 10, 2024 · For more on this see at Poincaré duality algebra. Poincaré duality is the mechanism behind Umkehr maps / push-forward in generalized cohomology: given a map of spaces f: X → Y f \colon X \to Y which enjoy Poincaré duality with respect to some generalized cohomology theory R R, one can pass from the canonically given pullback morphism.
May 11, 2024 · Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory ...
May 22, 2024 · Annales Henri Poincaré - A solution of the classical Yang–Baxter equation associated with the queer Lie superalgebra is constructed in terms of Hermite theta functions.
