Rocky Mountain Journal of Mathematics

Semigroup compactifications of Zappa products

H.D. Junghenn and P. Milnes

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Abstract

A group $G$ with subgroups $S$ and $T$ satisfying $G = ST$ and $S\cap T = \{e\}$ gives rise to functions $[t,s] \in S$ and $\\lt t,s\> \in T$ such that $(st)(s't') = (s[t,s'])(\\lt t,s'\>t')$. This notion may be extended to arbitrary semigroups $S$, $T$ with identities, producing the Zappa product of $S$ and $T$, a generalization of direct and semidirect product. Necessary and sufficient conditions are given for a semigroup compactification of a Zappa product $G$ of topological semigroups $S$ and $T$ to be canonically isomorphic to a Zappa product of compactifications of $S$ and $T$. The result is applied to various types of compactifications of $G$, including the weakly almost periodic and almost periodic compactifications.

Article information

Source
Rocky Mountain J. Math., Volume 44, Number 6 (2014), 1903-1921.

Dates
First available in Project Euclid: 2 February 2015

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1422885100

Digital Object Identifier
doi:10.1216/RMJ-2014-44-6-1903

Mathematical Reviews number (MathSciNet)
MR3310954

Zentralblatt MATH identifier
1311.22003

Citation

Junghenn, H.D.; Milnes, P. Semigroup compactifications of Zappa products. Rocky Mountain J. Math. 44 (2014), no. 6, 1903--1921. doi:10.1216/RMJ-2014-44-6-1903. https://projecteuclid.org/euclid.rmjm/1422885100


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References

  • J. Berglund, H. Junghenn and P. Milnes, Analysis on semigroups: Function spaces, compactifications, representations, John Wiley and Sons, New York, 1989.
  • K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications, Acta Math. 105 (1961), 63–97.
  • ––––, Almost periodic functions on semigroups, Acta Math. 105 (1961), 99–140.
  • H. Junghenn, Distal compactifications of semigroups, Trans. Amer. Math. Soc. 274 (1982), 379–397.
  • H. Junghenn and B. Lerner, Semigroup compactifications of semidirect products, Trans. Amer. Math. Soc. 265 (1981), 393–404.
  • M. Kunze, Lineare Parallelrechner, Interner Bericht, Tech. Hochschule, Darmstadt, 1982.
  • M. Landstad, On the Bohr compactification of a transformation group, Math. Z. 127 (1972), 167–178.
  • G. Mackey, Products of subgroups and projective multipliers, Coll. Math. Soc. Janos Bolyai 5 (1970), Hilbert Space Operators, Tihany, Hungary.
  • J. Szep, On the structure of groups which can be represented as the product of two subgroups, Acta Sci. Math. Szeged 12 (1950), 57–61.
  • G. Zappa, Sulla costruzione dei gruppi prodotto di due dati sottogruppi permutabili traloro, At. Sec. Cong. Mat. Ital., Bologna, 1942.