7,777 research outputs found
On a New Construction of Pseudo BL-Algebras
We present a new construction of a class pseudo BL-algebras, called kite
pseudo BL-algebras. We start with a basic pseudo hoop . Using two injective
mappings from one set, , into the second one, , and with an identical
copy with the reverse order we construct a pseudo BL-algebra
where the lower part is of the form and the upper one is
. Starting with a basic commutative hoop we can obtain even a
non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with
non-commuting negations. We describe the construction, subdirect irreducible
kite pseudo BL-algebras and their classification
Classifying crossed product C*-algebras
I combine recent results in the structure theory of nuclear C*-algebras and
in topological dynamics to classify certain types of crossed products in terms
of their Elliott invariants. In particular, transformation group C*-algebras
associated to free minimal Z^d-actions on the Cantor set with compact space of
ergodic measures are classified by their ordered K-theory. In fact, the
respective statement holds for finite dimensional compact metrizable spaces,
provided that projections of the crossed products separate tracial states.
Moreover, C*-algebras associated to certain minimal homeomorphisms of odd
dimensional spheres are only determined by their spaces of invariant Borel
probability measures (without a condition on the space of ergodic measures).
Finally, I show that for a large collection of classifiable C*-algebras,
crossed products by Z^d-actions are generically again classifiable.Comment: some corrections and explanations added; 22 pages; to appear in
American Journal of Mathematic
On -ary Lie algebras of type
These notes are devoted to the multiple generalization of a Lie algebra
introduced by A.M.Vinogradov and M.M.Vinogradov. We compare definitions of such
algebras in the usual and invariant case. Furthermore, we show that there are
no simple -ary Lie algebras of type for
Infinite index extensions of local nets and defects
Subfactor theory provides a tool to analyze and construct extensions of
Quantum Field Theories, once the latter are formulated as local nets of von
Neumann algebras. We generalize some of the results of [LR95] to the case of
extensions with infinite Jones index. This case naturally arises in physics,
the canonical examples are given by global gauge theories with respect to a
compact (non-finite) group of internal symmetries. Building on the works of
Izumi, Longo, Popa [ILP98] and Fidaleo, Isola [FI99], we consider generalized
Q-systems (of intertwiners) for a semidiscrete inclusion of properly infinite
von Neumann algebras, which generalize ordinary Q-systems introduced by Longo
[Lon94] to the infinite index case. We characterize inclusions which admit
generalized Q-systems of intertwiners and define a braided product among the
latter, hence we construct examples of QFTs with defects (phase boundaries) of
infinite index, extending the family of boundaries in the grasp of [BKLR16].Comment: 50 page
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