28 research outputs found
Tensor powers of adjoint representations ot classical Lie groups
Exploiting particular features of classical groups, simple constructions are
given for the irreducible constituents of the tensor square of the adjoint
modules and the leading terms in higher tensor powers. This provides an
independent confirmation of Vogel's general formulae, and alternative approach
to that in some recent papers.Comment: 17 pages. References to previous similar constructions would be
welcom
T-duality for principal torus bundles and dimensionally reduced Gysin sequences
We reexamine the results on the global properties of T-duality for principal
circle bundles in the context of a dimensionally reduced Gysin sequence. We
will then construct a Gysin sequence for principal torus bundles and examine
the consequences. In particular, we will argue that the T-dual of a principal
torus bundle with nontrivial H-flux is, in general, a continuous field of
noncommutative, nonassociative tori.Comment: 21 pages, typos correcte
Nonassociative tori and applications to T-duality
In this paper, we initiate the study of C*-algebras endowed with a twisted
action of a locally compact Abelian Lie group, and we construct a twisted
crossed product, which is in general a nonassociative, noncommutative, algebra.
The properties of this twisted crossed product algebra are studied in detail,
and are applied to T-duality in Type II string theory to obtain the T-dual of a
general principal torus bundle with general H-flux, which we will argue to be a
bundle of noncommutative, nonassociative tori. We also show that this
construction of the T-dual includes all of the special cases that were
previously analysed.Comment: 32 pages, latex2e, uses xypic; added more details on the
nonassociative toru
T-duality trivializes bulk-boundary correspondence: the parametrised case
We state a general conjecture that T-duality trivialises a model for the
bulk-boundary correspondence in the parametrised context. We give evidence that
it is valid by proving it in a special interesting case, which is relevant both
to String Theory and to the study of topological insulators with defects in
Condensed Matter Physics.Comment: 24 pages. Revise
Parametrised strict deformation quantization of C*-bundles and Hilbert C*-modules
In this paper, we use the parametrised strict deformation quantization of
C*-bundles obtained in a previous paper, and give more examples and
applications of this theory. In particular, it is used here to classify
H_3-twisted noncommutative torus bundles over a locally compact space. This is
extended to the case of general torus bundles and their parametrised strict
deformation quantization. Rieffel's basic construction of an algebra
deformation can be mimicked to deform a monoidal category, which deforms not
only algebras but also modules. As a special case, we consider the parametrised
strict deformation quantization of Hilbert C*-modules over C*-bundles with
fibrewise torus action.Comment: 13 page
Nonassociative strict deformation quantization of C*-algebras and nonassociative torus bundles
In this paper, we initiate the study of nonassociative strict deformation
quantization of C*-algebras with a torus action. We shall also present a
definition of nonassociative principal torus bundles, and give a classification
of these as nonassociative strict deformation quantization of ordinary
principal torus bundles. We then relate this to T-duality of principal torus
bundles with -flux. We also show that the Octonions fit nicely into our
theory.Comment: 15 pages, latex2e, exposition improved, to appear in LM