88 research outputs found
Radikalbegriffe für Halbgruppen mit Nullelement, die dem Jacobsonschen ringtheoretischen Radikal ähnlich sind
The Gelfand map and symmetric products
If A is an algebra of functions on X, there are many cases when X can be
regarded as included in Hom(A,C) as the set of ring homomorphisms. In this
paper the corresponding results for the symmetric products of X are introduced.
It is shown that the symmetric product Sym^n(X) is included in Hom(A,C) as the
set of those functions that satisfy equations generalising f(xy)=f(x)f(y).
These equations are related to formulae introduced by Frobenius and, for the
relevant A, they characterise linear maps on A that are the sum of ring
homomorphisms. The main theorem is proved using an identity satisfied by
partitions of finite sets.Comment: 14 pages, Late
Bi-branes: Target Space Geometry for World Sheet topological Defects
We establish that the relevant geometric data for the target space
description of world sheet topological defects are submanifolds - which we call
bi-branes - in the product M1 x M2 of the two target spaces involved. Very much
like branes, they are equipped with a vector bundle, which in backgrounds with
non-trivial B-field is actually a twisted vector bundle. We explain how to
define Wess-Zumino terms in the presence of bi-branes and discuss the fusion of
bi-branes.
In the case of WZW theories, symmetry preserving bi-branes are shown to be
biconjugacy classes. The algebra of functions on a biconjugacy class is shown
to be related, in the limit of large level, to the partition function for
defect fields. We finally indicate how the Verlinde algebra arises in the
fusion of WZW bi-branes.Comment: 29 page
Homomorphe Abbildungen auf Gruppen und das Radikal rad S Dem, 25. Jahrestag der DDR gewidmet
Radikalbegriffe für Halbgruppen mit Nullelement, die dem JACOBSONschen ringtheoretischen Radikal ähnlich sind
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