Abstract
We describe right-hand skew Boolean algebras in terms of a class of presheaves of sets over Boolean algebras called Boolean sets, and prove a duality theorem between Boolean sets and étalé spaces over Boolean spaces.
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Doctor H. P.: The categories of Boolean lattices, Boolean rings and Boolean spaces. Canad. Math. Bull. 7, 245–252 (1964)
Kudryavtseva G.: A refinement of Stone duality to skew Boolean algebras. Algebra Universalis 67, 397–416 (2012)
Kudryavtseva G.: A dualizing object approach to noncommutative Stone duality. J. Austral. Math. Soc. 95, 383–403 (2013)
Kudryavtseva G., Lawson M. V.: The structure of generalized inverse semigroups. Semigroup Forum 89, 19–216 (2014)
Kudryavtseva, G., Lawson, M. V.: Etale actions and non-commutative Stone duality. (in preparation)
Lawson, M. V.: Inverse semigroups: the theory of partial symmetries. World Scientific, NJ (1998)
Lawson M. V.: A non-commutative generalization of Stone duality. J. Austral. Math. Soc. 88, 385–404 (2010)
Lawson M. V.: Non-commutative Stone duality: inverse semigroups, topological groupoids and \({C^\bigstar}\)-algebras. Internat. J. Algebra Comput. 22, 1250058 (2012)
Lawson M. V., Lenz D. H.: Pseudogroups and their etale groupoids. Adv. Math. 244, 117–170 (2013)
Leech J.: Skew Boolean Algebras. Algebra Universalis 27, 497–506 (1990)
Leech J.: Recent developments in the theory of skew lattices. Semigroup Forum 52, 7–24 (1996)
Mac Lane, S., Moerdijk, I.: Sheaves in Geometry and Logic. Springer, New York (1994)
Stone M.H.: Applications of the theory of Boolean rings to general topology. Trans. Amer. Math. Soc. 41, 375–481 (1937)
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Presented by M. Jackson.
The first author was partially supported by ARRS grant P1-0288, and the second by EPSRC grant EP/I033203/1.
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Kudryavtseva, G., Lawson, M.V. Boolean sets, skew Boolean algebras and a non-commutative Stone duality. Algebra Univers. 75, 1–19 (2016). https://doi.org/10.1007/s00012-015-0361-0
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DOI: https://doi.org/10.1007/s00012-015-0361-0