Group and Geometric Quotient Semiproducts

Steven Givant and Hajnal Andréka
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Steven Givant: Mills College, Department of Mathematics
Hajnal Andréka: Alfréd Rényi Institute of Mathematics, Institute of Mathematics, Hungarian Academy of Sciences

Chapter Chapter 9 in Simple Relation Algebras, 2017, pp 321-406 from Springer

Abstract: Abstract This chapter presents two concrete examples of the quotient semiproduct construction from Chapter 8 In the first example, the base algebras are algebras of subsets, or complexes, of groups under the usual set-theoretic Boolean operations and the relative operations induced by the group operations on complexes. I n the second example, the base algebras are algebras of complexes of projective geometries (augmented by an identity element) under the set-theoretic Boolean operations and the relative operations induced by the collinearity relation. In both cases, it is shown that a quotient semiproduct system can always be reduced to a corresponding system consisting of groups and group quotient isomorphisms, or geometries and geometric quotient isomorphisms, respectively. This reduction leads to substantial simplifications in terminology and notation.

Date: 2017
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DOI: 10.1007/978-3-319-67696-8_9

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