2,613 research outputs found
Magnetic translation groups as group extension
Extensions of a direct product T of two cyclic groups Z_n1 and Z_n2 by an
Abelian (gauge) group G with the trivial action of T on G are considered. All
possible (nonequivalent) factor systems are determined using the Mac Lane
method. Some of resulting groups describe magnetic translation groups. As
examples extensions with G=U(1) and G=Z_n are considered and discussed.Comment: 10 page
A loop group extension of the odd Chern character
We show that the universal odd Chern form, defined on the stable unitary
group , extends to the loop group in a way that is closed with respect
to an equivariant-type differential. This provides an odd analogue to the
Bismut-Chern form. We also describe the associated transgression form, the
so-called Bismut-Chern-Simons form, and explicate some properties it inherits
as a differential form on the space of maps of a cylinder into the stable
unitary group. As a corollary, we obtain the Chern character homomorphism from
odd K-theory to the periodic cohomology of the free loop space, represented
geometrically on the level of differential forms.Comment: 12 pages, comments welcom
A seven-term exact sequence for the cohomology of a group extension
In this paper, we construct a seven-term exact sequence involving the
cohomology groups of a group extension. Although the existence of such a
sequence can be derived using spectral sequence arguments, there is little
knowledge about some of the maps occuring in the sequence, limiting its
usefulness. Here we present a construction using only very elementary tools,
always related to the notion of conjugation in a group. This results in a
complete and usable description of all the maps, which we describe both on
cocycle level as on the level of the interpretations of low dimensional
cohomology groups (e.g. group extensions).Comment: Updated version, new cocycle description adde
- …