/sci/ - Science & Math

>>10749799
>tfw you don't know how to compute low dimensional homotopy groups of some space so you suspend it until they're all gone

>>9284631
>single book
No.
>Banach algebras
Any functional analysis.
>Affine Hecke algebra
Any mathematical text on conformal field theory.
>Exterior algebra
Any differential topology book.
>Koszul algebra
Any homological algebra text.
>Poisson algebra
Any classical mechanics text.
>Weyl algebra
Any mathematical text on quantum field theory.
>>9284936
Let [math]X[/math] be a [math]G[/math]-space and denote the action of [math]G[/math] on [math]X[/math] by [math]g \mapsto (x \mapsto g(x))[/math], then the [math]G[/math]-quotient is the space of orbits [math]\mathcal{O}_x = \{y \in X\mid y = g(x) \}[/math].
>>9287959
Let [math]f\in\mathcal{S}_c[/math] be a test function and suppose [math]\phi[/math] satisfies the equation [math]\phi'' + \phi = 0[/math], then [eqn]\int_K dxf(x)\phi(x) = -\int_K dxf(x)\phi''(x) \rightarrow_{x \rightarrow nx} -\frac{1}{n} \int_K d(nx) f(nx)\phi''(nx) = -\frac{1}{n}\int_K dx f(x)\phi''(x) = -\frac{1}{n}\int_K dx f(x)\phi(x) \rightarrow 0[/eqn]
Remember that scalings of compact sets are still compact so [math]f_n(x)\equiv f(nx) \in \mathcal{S}_c[/math].