457 research outputs found
The Montgomery and Joye Powering Ladders are Dual
Hitherto the duality between left-to-right and right-to-left exponentiation algorithms has been a loosely defined concept. Recently, the author made the definition precise by adding requirements on space usage and operation types. Here it is shown that the Montgomery and Joye powering ladders are dual in this sense. Several versions of these algorithms are derived naturally with a cost-free, natural, built-in blinding mechanism as a side channel counter-measure
On Low-Dimensional Locally Compact Quantum Groups
Continuing our research on extensions of locally compact quantum groups, we
give a classification of all cocycle matched pairs of Lie algebras in small
dimensions and prove that all of them can be exponentiated to cocycle matched
pairs of Lie groups. Hence, all of them give rise to locally compact quantum
groups by the cocycle bicrossed product construction. We also clarify the
notion of an extension of locally compact quantum groups by relating it to the
concept of a closed normal quantum subgroup and the quotient construction.
Finally, we describe the infinitesimal objects of locally compact quantum
quantum groups with 2 and 3 generators - Hopf *-algebras and Lie bialgebras.Comment: 64 pages, LaTeX, needs class-file irmadegm.cls. To appear in Locally
Compact Quantum Groups and Groupoids. Proceedings of the Meeting of
Theoretical Physicists and Mathematicians, Strasbourg, February 21 - 23, 200
The bicrossed product construction for locally compact quantum groups
The cocycle bicrossed product construction allows certain freedom in
producing examples of locally compact quantum groups. We give an overview of
some recent examples of this kind having remarkable properties
Renormalization : A number theoretical model
We analyse the Dirichlet convolution ring of arithmetic number theoretic
functions. It turns out to fail to be a Hopf algebra on the diagonal, due to
the lack of complete multiplicativity of the product and coproduct. A related
Hopf algebra can be established, which however overcounts the diagonal. We
argue that the mechanism of renormalization in quantum field theory is modelled
after the same principle. Singularities hence arise as a (now continuously
indexed) overcounting on the diagonals. Renormalization is given by the map
from the auxiliary Hopf algebra to the weaker multiplicative structure, called
Hopf gebra, rescaling the diagonals.Comment: 15 pages, extended version of talks delivered at SLC55 Bertinoro,Sep
2005, and the Bob Delbourgo QFT Fest in Hobart, Dec 200
Asymmetric Cosets
The aim of this work is to present a general theory of coset models G/H in
which different left and right actions of H on G are gauged. Our main results
include a formula for their modular invariant partition function, the
construction of a large set of boundary states and a general description of the
corresponding brane geometries. The paper concludes with some explicit
applications to the base of the conifold and to the time-dependent Nappi-Witten
background.Comment: 34 pages, LaTeX, 8 figures, 1 table, v2: references added, v3: typos
correcte
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