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29m
comment Generators and relations as a functor
A good example might be of use as well.
30m
comment Generators and relations as a functor
Let's try to figure out part of it and put it into the question, and then have the rest of it as an answer. First bit that should be in the question: A functor from which category into which? (At least give a rough guess)
32m
answered Arrow between endofunctors over a symmetric monoidal category.
2h
awarded  Citizen Patrol
Mar
25
revised From the representation category of a Lie group and the representation on a homogeneous space, can we reconstruct the stabiliser subgroup reps?
deleted 15 characters in body
Mar
25
revised From the representation category of a Lie group and the representation on a homogeneous space, can we reconstruct the stabiliser subgroup reps?
Added some background info for category theorists.
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
Ah, so already $\mathbb{C}[\mathbb{Z}_4] \cong \mathbb{C}[\mathbb{Z_2} \times \mathbb{Z}_2]$? I wonder whether these kind of isomorphisms are also equivalences of representation categories.
Mar
23
accepted Are there homomorphisms of group algebras that don't come from a group homomorphism?
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
That sounds interesting! You say "it is well known", but when I search for dihedral group, group algebra and quaternions, I can't find anything about this algebra isomorphism.
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
@Dustan, it seems I'm not familiar enough. How does the isomorphism you mean look like?
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
How is sending 1 to anything else than 1 an automorphism?
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
@Dustan, That's what I suspected, but I'm trying since half an hour. Maybe I'm looking at the wrong groups...
Mar
23
comment Are there homomorphisms of group algebras that don't come from a group homomorphism?
That's got to do with compact Lie groups, is it applicable to finite groups?
Mar
23
asked Are there homomorphisms of group algebras that don't come from a group homomorphism?
Mar
19
comment Gaussian integral asymptotics
With $y := x^2/4 \implies \mathrm{d}x = x\mathrm{d}x/2$, substitute to arrive at $\int_{2\sqrt{m}}^\infty e^{-\frac{x^2}{4}}x^m\mathrm{d}x = \int_{2\sqrt{m}}^\infty \frac{1}{2}e^{-y}y^{\frac{m+1}{2}}\mathrm{d}x$. Maybe this incomplete Gamma function can be approximated? The asymptotics of the Gamma function is well known.
Mar
19
comment Gaussian integral asymptotics
@AntonioVargas It doesn't look like the Laplace method because the integral boundaries are moving.
Mar
19
comment Vector Space of Lie Algebra
"I am a physics student, and hence not able to get a concrete mathematical structure of these things." Do you think that physics students don't have to learn maths properly or aren't able to? I encourage you to learn mathematics rigorously first, and then understand the physical motivation behind it.
Mar
19
comment How do I compute speed based on acceleration and drag?
And then integrate $v(t) = \int a(t) - d_1v(t)^2 \mathrm{d}t$, which can be hard, depending on $a$. Or are you simulating on a computer?
Mar
19
answered Showing that if there exist isometries $S_1,S_2 \in L(V)$ such that $T_1 = S_1T_2S_2$, then $T_1$ and $T_2$ have the same singular values.
Mar
19
comment function application order
Can you make your question more specific? It sounds sort of interesting, but I don't understand what you're asking.