22,796 research outputs found
Twisted algebras and Rota-Baxter type operators
We define the concept of weak pseudotwistor for an algebra in a
monoidal category , as a morphism in , satisfying some axioms ensuring that is also an algebra in . This concept generalizes the
previous proposal called pseudotwistor and covers a number of exemples of
twisted algebras that cannot be covered by pseudotwistors, mainly examples
provided by Rota-Baxter operators and some of their relatives (such as Leroux's
TD-operators and Reynolds operators). By using weak pseudotwistors, we
introduce an equivalence relation (called "twist equivalence") for algebras in
a given monoidal category.Comment: 15 pages; continues arXiv:math/0605086 and arXiv:0801.2055, some
concepts from these papers are recalled; we added a Note and some references.
In this final version, accepted for publication in J. Algebra Appl., the
title has been slighty modified and few little things have been adde
Asymmetric Orbifolds, Non-Geometric Fluxes and Non-Commutativity in Closed String Theory
In this paper we consider a class of exactly solvable closed string flux
backgrounds that exhibit non-commutativity in the closed string coordinates.
They are realized in terms of freely-acting asymmetric Z_N-orbifolds, which are
themselves close relatives of twisted torus fibrations with elliptic
Z_N-monodromy (elliptic T-folds). We explicitly construct the modular invariant
partition function of the models and derive the non-commutative algebra in the
string coordinates, which is exact to all orders in {\alpha}'. Finally, we
relate these asymmetric orbifold spaces to inherently stringy Scherk-Schwarz
backgrounds and non-geometric fluxes.Comment: 30 page
Tied Monoids
We construct certain monoids, called tied monoids. These monoids result to be
semidirect products finitely presented and commonly built from braid groups and
their relatives acting on monoids of set partitions. The nature of our monoids
indicate that they should give origin to new knot algebras; indeed, our tied
monoids include the tied braid monoid and the tied singular braid monoid, which
were used, respectively, to construct new polynomial invariants for classical
links and singular links. Consequently, we provide a mechanism to attach an
algebra to each tied monoid. To build the tied monoids it is necessary to have
presentations of set partition monoids of types A, B and D, among others. For
type A we use a presentation due to FitzGerald and for the other type it was
necessary to built them.Comment: 47 page
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