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visits member for 2 years, 6 months
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PhD

Interests:

Ring and module theory

Clifford algebra/Geometric algebra

Mathematical physics

Applications of abstract algebra

Misc: Let $m$ and $n$ be integers in the ring of integers. Show that if $m\mathbb Z$ contains $n\mathbb Z$ if and only if $m$ divides $n$


Oct
24
comment Quaternion - Spinor relationship?
@JCW There are no doubt hundreds of web pages explaining the connection, but I know that many of them are written by physicists, and hence long, involved and example-centric. I bet there's a terse algebraic bundling, but unfortunately I haven't internalized spinors enough yet to say what it is. I used to think they were related to simple modules of Clifford algebras, but I never learned the details well.
Oct
24
comment Quaternion - Spinor relationship?
@JCW Actually I had meant to include the link that led me to that page too. I added it also.
Oct
24
revised Quaternion - Spinor relationship?
added 207 characters in body
Oct
24
answered Quaternion - Spinor relationship?
Oct
24
answered Equivalent definitions of an algebra over a ring
Oct
24
comment Prove the set, {y ∈ X | r ≤ d(x,y) ≤ s}, is closed
Do you believe in closed balls and open balls? You could make it the intersection of a closed ball with the complement of an open ball: a closed set.
Oct
23
comment prove that if $\exists a\in A\space:\space stb(a)\not=\{e\}$ then the action is unfaithful
@AmitaiYuval OK: replacing $A$ with a singleton is simpler, but much simpler might be an overstatement :)
Oct
23
revised A counterexample to $Ae\simeq Ae^{\prime}\to A(1-e)\simeq A(1-e^{\prime})$
edited tags
Oct
23
revised A counterexample to $Ae\simeq Ae^{\prime}\to A(1-e)\simeq A(1-e^{\prime})$
deleted 18 characters in body
Oct
23
comment Krull-Schmidt theorem and internally cancellable modules?
Thanks for reopening it. Glancing at the link, I think the example I'm giving is different from the ones given there.
Oct
23
answered A counterexample to $Ae\simeq Ae^{\prime}\to A(1-e)\simeq A(1-e^{\prime})$
Oct
23
answered prove that if $\exists a\in A\space:\space stb(a)\not=\{e\}$ then the action is unfaithful
Oct
23
comment Is this a proper way to prove simple geometrical result?
@user3365247 Maybe saying "congruent to itself" is hiding the trick that it's actually congruent to its reflection across the vertical axis. In that process, the two angles in question get overlaid, and it becomes clear they're congruent. Subtle difference, maybe :)
Oct
23
comment Is this a proper way to prove simple geometrical result?
At first I was looking at the wrong angle in step 3. I see now that they were talking about $\angle ABC$ being congruent to itself.
Oct
23
comment Mathematical aspects of General Relativity
I'm well aware of the status of GA. In my past year or two of reading, the areas of math most relevant to spinor and twistor theory were Lie theory, differential geometry and GA. The operations involved are mainly noncommutative, so I haven't noticed any AG. but perhaps there is some sheaf and stack theoretic stuff I simply didn't recognize. That theory is very general, after all. I can't find much on heaven spaces: the one source I found so far is mainly differential geometry.
Oct
22
comment Mathematical aspects of General Relativity
Are you sure you don't mean 'geometric algebra' instead of algebraic geometry? If you really do mean AG, could you give concrete examples?
Oct
22
comment Division Rings and trivial ideals
@Charles I can easily see the answer when $R^2=0$ or $R$ has identity. I'm basically stuck on $R^2=R$ for a ring without identity.
Oct
22
comment Division Rings and trivial ideals
@Charles That is correct (in a ring with identity) but it's totally different from the zero divisor comment :)
Oct
22
comment Abstract Algebra and Chess
Some moves in chess are irreversible, so considering positions modified by moves is at best a semigroup. If you're willing to allow an "identity move" then maybe a monoid. There could be some more subtle use of a group somewhere, but I'm just stating the obvious about the most obvious idea of a position space being operated on by moves.
Oct
22
comment Abstract Algebra and Chess
Did you have some motivating connection or did you just pick two random things you like and are fishing for a connection?