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Results tagged with abelian-groups
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user 58211
For questions about groups whose elements commute.
2
votes
0
answers
61
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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
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
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
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
2
votes
1
answer
143
views
Intermediate lattices $C\mathbb{Z}^n \subseteq \Lambda \subseteq \mathbb{Z}^n$
Let $C \in \mathfrak{gl}(\mathbb{Z},n)$ be a symmetric full rank integer valued matrix (in my case its the symmetric part of a Cartan matrix).. Let $\Lambda \subseteq \mathbb{Z}^n$ be a full rank sub …
- 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 …
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