5,104 reputation
31852
bio website iaz.uni-stuttgart.de/…
location Stuttgart, Germany
age 28
visits member for 3 years, 3 months
seen 20 hours ago

Post-Doc working in representation theory


A proud contributor to the Crusade of Answers - more info on meta. Fellow knights include Lord_Farin, ˈjuː.zɚ79365 and rschwieb.

We are recruiting: just visit the chat room.


1d
reviewed Close What are some mathematically productive ways to waste time?
1d
reviewed Close Evaluate the given integral along the given (positively oriented) circle.
1d
reviewed Close If $|f|+|g|$ is constant then each of $f, g$ is constant
1d
reviewed Close How to continue on proving that rank (A+B) ≤ Rank A + Rank B?
1d
revised For a simple nonabelian group every automorphism with $xf(x)=f(x)x$ is trivial.
more descriptive title, LaTeX
1d
reviewed Leave Open Permutation of positive real numbers
1d
reviewed Leave Open Why do we need to learn Set Theory?
1d
reviewed Close Evaluating a complex integral using the Cauchy integral formula
1d
reviewed Leave Open Borel measurable functions $f:[0,1]\to[0,\infty)$ which cannot be expressed as pointwise limit of nondecreasing sequence of step functions
1d
awarded  Constituent
Dec
8
awarded  Caucus
Nov
26
awarded  Good Question
Nov
3
comment How to compute $Ext_A^{1}(S_1, S_2)$ and $Ext_A^{1}(S_2, S_1)$?
$\operatorname{dim}\operatorname{Ext}^1(S_i,S_j)=$ number of arrows $i \to j$
Nov
2
comment How to compute $Ext_A^{1}(S_1, S_2)$ and $Ext_A^{1}(S_2, S_1)$?
In fact $A$ has infinite projective dimension, not projective dimension $1$.
Oct
21
awarded  Revival
Oct
12
comment Suppose $A$ is an invertible matrix. Prove that $det(A^{-2}) = 1/(det(A))^2$
Yes, if you already know that $\operatorname{det}(AB) =\operatorname{det}(A)\operatorname{det}(B)$.
Oct
10
answered what is dimension of orthogonal complement of a subspace of a vector space.
Oct
5
comment Let $V=V_{1}⊕ ⋯ ⊕ V_{n}$ be semisimple. $U$ irreducible. Show that $\dim_{k} (Hom_A(U,V)) $ is equal to the number of $V_i$ equivalent to $U$.
possible duplicate of Remark 3.1.3 from Introduction to Representation Theory from Pavel Etingof
Oct
3
comment Let $A=k[x]$ and let $V=k[x]/\big((x-λ )^{n} \big)$ for some $λ \in k$ and $n\in \Bbb{N}$. Then $V$ is indecomposable.
If you don't feel comfortable with the internal direct sum, just replace it with the ordinary sum: $U+U':= \{u+u': u\in U, u'\in U'\}$. The argument woks just as fine.
Oct
1
comment Let $A=k[x]$ and let $V=k[x]/\big((x-λ )^{n} \big)$ for some $λ \in k$ and $n\in \Bbb{N}$. Then $V$ is indecomposable.
$I\oplus I$ is not an internal direct sum, it has a non-trivial intersection.