Noah Snyder

Bloomington, Indiana

sbseminar.wordpress.com

Age: 35

Assistant Professor at Indiana University, working on tensor categories and their relationships to operator algebras and topology.
Feb
10
awarded Good Question
Feb
4
comment Can the ribbon category of f.d. reps of $\mathcal{U}_q(\mathfrak{sl}(2))$ be modified so the twist is trivial on the vector representation?
The point here is roughly that central character gives a grading on representations, and so elements of the center of the corresponding Lie group give you the ways of changing ribbon structure. For SL the center is finite and so you only get a few ribbon structures, but for GL the center is the scalars and so you can change ribbon structure at the vector rep however you want. The ribbon structure won't be trivial everywhere, in particular the quantum determinant will no longer have trivial ribbon element (which is why this ribbon structure doesn't descend to SL).
Feb
1
revised What constitutes a declarable conflict of interest in gender studies?
edited body
Feb
1
comment What constitutes a declarable conflict of interest in gender studies?
In addition to being conflicted by people who pay you, you're also usually conflicted with immediate family and current or former romantic partners, or with anyone who those people have a financial relationship.
Jan
30
comment Advisor likes MS Word, I like LaTeX
What field are you in? Is one of LaTeX or Word standard in your field? My opinion is a bit different depending on which of you is the weird one.
Jan
29
accepted Technical issue in the approach to Lie groups taken in Brian C. Hall's book
Jan
29
awarded gr.group-theory
Jan
28
awarded Nice Answer
Jan
28
revised Technical issue in the approach to Lie groups taken in Brian C. Hall's book
added 11 characters in body
Jan
28
answered Technical issue in the approach to Lie groups taken in Brian C. Hall's book
Jan
28
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
@TheoJohnson-Freyd: Thanks! It was just a bit weird that I kept finding that same detail skipped over and over again when trying to look this up.
Jan
27
answered Technical issue in the approach to Lie groups taken in Brian C. Hall's book
Jan
27
awarded Nice Question
Jan
27
awarded Inquisitive
Jan
27
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
@VítTuček: I think you're right, that works. The key fact is that the adjoint form is automatically a closed subgroup of $\mathrm{GL}(\mathfrak{g})$ when $\mathfrak{g}$ is simple.
Jan
27
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
@TheoJohnson-Freyd: Of course you're right that $\mathrm{SL}_2(R)$ is not compact, but it shows that you need to use compactness somehow in that step. While you're here, why is the image of Ad a closed subgroup in Prop 7.2.1.6 from the Lie groups notes on your webpage?
Jan
26
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
@VítTuček: Does that characterization always yield a matrix compact Lie group?
Jan
26
comment Technical issue in the approach to Lie groups taken in Brian C. Hall's book
One approach would be to show that compact matrix groups do have matrix universal covers, but as far as I can tell that's hard (Peter-Weyl). Another possible approach is to show that the root system breaks up as a direct sum and then use the summand root systems to explicitly realize each of the summands as a compact-semisimple algebra.
Jan
26
revised Technical issue in the approach to Lie groups taken in Brian C. Hall's book
added 2 characters in body
Jan
26
asked Technical issue in the approach to Lie groups taken in Brian C. Hall's book
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