All Questions
4 questions
2
votes
2
answers
265
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Commuting nilpotent matrices and conjugation isomorphisms
Trying to study isomorphism classes of certain commutative Artinian $\mathbb{C}$-algebras I was lead to the following problem about matrices.
Suppose you have a (non-zero) nilpotent matrix $A\in M_n(\...
0
votes
1
answer
452
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Conjugacy in the quaternion group
Let $G$ be a non-commutative group, and suppose we are given two elements $x, y \in G$ which are conjugate, i.e. we know there exists some $z \in G$ such that $zxz^{-1} = y$. Can we find $z$ given $x$ ...
1
vote
0
answers
179
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Matrix factorizations over $GL_2$ of a real quadratic ring of integers
tl;dr: The groups $GL_2(K)$, or $SL_2(K)$, where $K = \mathbb{C,R}$ admits several factorizations (the polar decomposition,
the KAN decomposition, the Schur triangular form, etc). Those
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4
votes
1
answer
284
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When is Out$(SL_n(R))$ a torsion group ?
This question is a follow up question to this question. So my question is:
For which rings $R$ (commutative, with unit) (and which integers $n$) is $Out(SL_n(R))$ a torsion group? A consequence of ...