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2 votes
2 answers
265 views

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(\...
amateur's user avatar
  • 375
0 votes
1 answer
452 views

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 $x$ ...
Gautam's user avatar
  • 1,703
1 vote
0 answers
179 views

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 ...
Adrián González Pérez's user avatar
4 votes
1 answer
284 views

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 ...
HenrikRüping's user avatar