507 research outputs found
Polynomial fusion rings of W-extended logarithmic minimal models
The countably infinite number of Virasoro representations of the logarithmic
minimal model LM(p,p') can be reorganized into a finite number of
W-representations with respect to the extended Virasoro algebra symmetry W.
Using a lattice implementation of fusion, we recently determined the fusion
algebra of these representations and found that it closes, albeit without an
identity for p>1. Here, we provide a fusion-matrix realization of this fusion
algebra and identify a fusion ring isomorphic to it. We also consider various
extensions of it and quotients thereof, and introduce and analyze commutative
diagrams with morphisms between the involved fusion algebras and the
corresponding quotient polynomial fusion rings. One particular extension is
reminiscent of the fundamental fusion algebra of LM(p,p') and offers a natural
way of introducing the missing identity for p>1. Working out explicit fusion
matrices is facilitated by a further enlargement based on a pair of mutual
Moore-Penrose inverses intertwining between the W-fundamental and enlarged
fusion algebras.Comment: 48 page
Factorization properties of universal algebras
Includes abstract.Includes bibliographical references (leaves 92-95).This dissertation deals with algebraic structures that can be written as the product of directly indecomposable algebras in a unique way up to isomorphism, known as the Unique Factorization Property. Here we undertake the task of collecting all the major results discovered by a few mathematicians (A. Tarski, B. J´onsson, R. Mckenzie, C. Chang, G. Birkhoff, L. Lovasz, etc.) over the past century. Another goal of this thesis was to highlight important and to introduce fresh techniques. The scope of most of them is still unknown and hopefully they can be utilised further to yield new results to revive this beautiful branch of mathematics
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