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Results tagged with gr.group-theory
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user 58211
Questions about the branch of algebra that deals with groups.
2
votes
0
answers
61
views
Alternating $n$-homomorphism on abelian group is skew of $n$-cocycle
Let $A$ be a finitely generated abelian group. Let $c$ be a 2-cocycle on $A$, where $A$ acts trivially on $\mathbb{C}^\times$. It is well-known that the skew-map
$$ c(a_1,a_2) \longmapsto \frac{c(a_1, …
- 1,527
2
votes
1
answer
240
views
Recurrence relation for number of reduced words of longest element in $S_n$
Is there any recurrence relation known for the number of reduced words of the longest element in $S_n$ (not commutation classes)?
Edit: Sorry for unaccepting the answer, but I realized that I really …
- 1,527
1
vote
1
answer
138
views
Non-degeneracy of product of group pairings
For $G$ finite abelian group, let $\eta,\omega:G \times G \to \mathbb{C}^\times$ be group pairings. What can I say about the (non-)degeneneracy of the product pairing $\eta \cdot \omega$ in terms of …
- 1,527
0
votes
1
answer
113
views
Orthogonal idempotents with sum equal to 1 in $k[G]$ span sub-Hopf algebra
Let $G$ be a finite group. Let $B$ be a set of orthogonal non-zero idempotents with $|B| \leq |G|$, s.t. $\sum_{b \in B}b =1_{kG}$. Is it known if $B$ spans a sub-Hopf algebra $kH \subseteq kG$?
- 1,527
1
vote
0
answers
81
views
Symmetric analogue of "alternating bihomomorphism is skew of 2-cocycle" theorem
Let $G$ be a finite abelian group. It is well-known that every alternating bihomomorphism $\Omega:G\times G \to \mathbb{C}^\times$ arises as the skew $\kappa/\kappa^T$ of a 2-cocycle $\kappa \in Z^2(G …
- 1,527
4
votes
0
answers
66
views
Is the associated grouplike $\gamma=uS(u)^{-1}$ of a quasi-triangular Hopf algebra always th...
Let $(H,R)$ be a finite-dimensional quasi-triangular Hopf algebra, lets say generated by group-like and skew-primitive elements (I actually need it for $H$ fin. dim. pointed with $G(H)$ abelian). Let …
- 1,527
2
votes
0
answers
89
views
Alternating bihomomorphism is skew of 2-cocycle - relative situation
Let $G$ be a finite abelian group. It is well-known that every alternating bihomomorphism $\Omega:G\times G \to \mathbb{C}^\times$ (i.e. $\Omega(g,g)=1$) arises as the skew $\kappa/\kappa^T$ of a 2-c …
- 1,527
4
votes
1
answer
192
views
Is there a good notion of kernels of quadratic forms on abelian groups?
Let $G$ be an abelian group and let $q:G \to \mathbb{Q/Z}$ be a quadratic form, i.e. $q(a)=q(-a)$ and $b(x,y)=q(x+y)-q(x)-q(y)$ is a bihomomorphism. On vector spaces, when people speak about the kerne …
- 1,527