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Aug
23
comment Representation of a group, and finite index subspaces
It should also help you to observe that $U$ is spanned by $\{e_{ghg^{-1}}-e_h: g,h \in G\}$.
Aug
23
comment Representation of a group, and finite index subspaces
Let $g_1,\ldots,g_m$ lie in distinct conjugacy classes of $G$. You should try to prove that $e_{g_1}+U,\ldots,e_{g_m}+U$ are linearly independent, so $m \leq n$. Then prove that if $g_1,\ldots,g_m$ are a complete set of conjugacy class reps, the $e_{g_i}+U$ span $V/U$ so $n \leq m$.
Aug
22
comment Are any two groups of order 23 isomorphic to each other?
What do you know about groups of prime order?
Aug
21
reviewed Approve suggested edit on Find a equation of a normal vector from point A to the plane
Aug
20
reviewed Approve suggested edit on Special solutions to Ax = 0
Aug
15
reviewed Approve suggested edit on Calculating the angle for a path between two nodes in a graph
Aug
15
reviewed Reject suggested edit on How does one solve $ y' = ( {2+\sqrt x})/({2+\sqrt y})$?
Aug
15
reviewed Approve suggested edit on How does one solve $ y' = ( {2+\sqrt x})/({2+\sqrt y})$?
Aug
14
comment What do the equations on this gate mean or relate to?
Surely the second one is an error...
Aug
13
comment Identities that connect antipode with multiplication and comultiplication
Try expressing the proof diagrammatically, you probably find it works anywhere.
Aug
12
comment Identities that connect antipode with multiplication and comultiplication
These are Hopf algebra objects in the category of vector spaces, I don't know a reference for more general categories, possibly the ncatlab has something.
Aug
12
answered Is there a listing of natural numbers with their properties?
Aug
12
answered Identities that connect antipode with multiplication and comultiplication
Aug
7
reviewed Approve suggested edit on Symmetry group of the vector field $V=x \partial /\partial x + y \partial /\partial y$
Aug
7
comment how do you find the modular inverse
en.wikipedia.org/wiki/Modular_multiplicative_inverse
Aug
7
reviewed Approve suggested edit on Convergence in $C(X)$ is uniform convergence.
Aug
6
reviewed Approve suggested edit on Finding the instantaneous rate of change of the function $f(x)=-x^2+4x$ at $x=5$
Aug
6
comment Toral sub algebra
You have two Lie algebras in play: one called $L$ and another, $T$, its toral subalgebra, with Killing forms $\kappa_L$ and $\kappa_T=0$ respectively. The restriction of $\kappa_L$ to $T$ means the bilinear form $T\times T \to \mathbb{C}$ (or whichever field you work over) sending $(s,t)$ to $\kappa_L(s,t)$. This is not necessarily the same as $\kappa_T$, and in fact is nondegenerate if $L$ is semisimple.
Aug
5
comment Toral sub algebra
The Killing form of the toral subalgebra is not nondegenerate, indeed the Killing form of any abelian Lie algebra $L$ is identically zero because $\operatorname{ad}(x)$ is the zero map for any $x \in L$. Perhaps you're confusing the Killing form of the torus with the Killing form of the big algebra restricted to the torus; they're different.
Jul
23
revised When does $n$-dimensional algebra have $m$-dimensional faithful representation?
edited title