Reputation
5,468
Next privilege 10,000 Rep.
Access moderator tools
Badges
1 17 33
Newest
 Nice Answer
Impact
~50k people reached

8h
revised Frobenius complement/kernel of an infinite group
added 30 characters in body
16h
revised Frobenius complement/kernel of an infinite group
added 486 characters in body
21h
comment Set of Special Unitary Matrices that are dense in SU(4) and obey certain relations
If you neglect the third relation, the abstract group with the first two relations is the Artin braid group $B_N$ on $N$ letters. For $N=5$, there are certainly representations (The Burau representation) into $U(h)$ for suitable Hermitian forms $h$ in four variables, whose projection into $U(4)$ (a compact group) contains $SU(4)$ in their closure. See a recent paper by Curt Mcmullen (Braid groups and Hodge theory, Math Annalen ) where such constructions are given
Feb
5
revised odd length Chevalley relations (in rank two)
the "unipotent radical" is of a Borel subgroup and not the algebraic group (the latter is reductive and has no unipotent radical). Edited accordingly
Feb
4
answered References about the matrix generators of the finite subgroups of the orthogonal group O(4)
Jan
28
comment is there a criterion for a two-generator subgroup of $PL(2,K)$ to be a cocompact lattice?
If this is what you want to know, that should be your question: how to prove that the element $\gamma$ has its eigenvalues in $K$? The proof is the same as for reals!
Jan
12
revised Maximal split torus of universal chevalley group
edited title
Jan
4
revised Frobenius complement/kernel of an infinite group
added 284 characters in body
Jan
4
comment Frobenius complement/kernel of an infinite group
@denis: I have added a line about the infinitude of $N$. There are unipotent elements in $G$, and they can never conjugate into $H$. Why does it say anything about the finite case?
Jan
4
revised Frobenius complement/kernel of an infinite group
edited body
Jan
4
comment Frobenius complement/kernel of an infinite group
@ denis. OOps! Pls convey my apologies to your uncle.
Jan
4
answered Frobenius complement/kernel of an infinite group
Jan
3
comment Metaplectic groups over non-archimedean local fields of characteristic>2
@jim: the symplectic group over ${\mathbb R}$ is not simply connected (has $\mathbb Z$ as fundamental group) but over $\mathbb C$, it is simply connected.
Jan
3
comment Metaplectic groups over non-archimedean local fields of characteristic>2
@jim: not over the reals ($SL_2({\mathbb R})$ is not simply connected) but over the complex numbers
Jan
2
comment Common zero of invariants of finite groups
Atiyah Mcdonald (commutative algebra) have a section on finite integral extension a
Jan
2
comment Common zero of invariants of finite groups
yes, it is true. You can extend a maximal ideal in the ring of invariants to a maximal ideal in the whole polynomial ring. Otherwise, the polynomial span of the smaller maximal ideal generates the unit ideal (nullstellensatz) , and by taking invariants under the finite group you get that the maximal ideal contains $1$. This argument holds for any finite integral extension
Dec
29
comment Unconventional types of induction
the letters $a_i$ are used both for roots and the coefficients of the polynomial $p(x)$.
Dec
29
revised Unconventional types of induction
since the letters $a_i$ was used both for coefficients as well as roots, I have changed the coefficients to $t_i$
Dec
26
reviewed Approve An elementary question about Gaussian primes
Dec
25
reviewed Approve limits-and-convergence tag wiki excerpt