منابع مشابه
Natural Dualities in Partnership
Traditionally in natural duality theory the algebras carry no topology and the objects on the dual side are structured Boolean spaces. Given a duality, one may ask when the topology can be swapped to the other side to yield a partner duality (or, better, a dual equivalence) between a category of topological algebras and a category of structures. A prototype for this procedure is provided by the...
متن کاملRegularising Natural Dualities
Given an algebra M we may adjoin an isolated zero to form an algebra M∞ satisfying all identities u ≈ v true in M for which u and v contain the same variables. Drawing on the structure theory of P lonka sums, we show that if M is a finite, dualisable algebra which is strongly irregular, then M∞ is also dualisable. Turning the construction of M∞ upside-down for the two-element left-zero band, we...
متن کاملNatural Dualities for Semilattice-based Algebras
While every finite lattice-based algebra is dualisable, the same is not true of semilattice-based algebras. We show that a finite semilattice-based algebra is dualisable if all its operations are compatible with the semilattice operation. We also give examples of infinite semilattice-based algebras that are dualisable. In contrast, we present a general condition that guarantees the inherent non...
متن کاملOptimal Natural Dualities. Ii: General Theory
A general theory of optimal natural dualities is presented, built on the test algebra technique introduced in an earlier paper. Given that a set R of finitary algebraic relations yields a duality on a class of algebras A = ISP(M), those subsets R′ of R which yield optimal dualities are characterised. Further, the manner in which the relations in R are constructed from those in R′ is revealed in...
متن کاملDUALITIES IN THE CLASSICAL SUPERGRAVITY LIMITS Dualisations, dualities and a détour via 4k+2 dimensions
Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (HodgeDirac-)Dualisation of gauge potentials exchanges Noether and topological charges, equations of motion and Bianchi identities, internal rigid symmetries and gauge symmetries, local trans...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2015
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2015.02.015