Towards a geometric theory for left loops

Karla Baez

Commentationes Mathematicae Universitatis Carolinae (2014)

  • Volume: 55, Issue: 3, page 315-323
  • ISSN: 0010-2628

Abstract

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In [Mwambene E., Multiples of left loops and vertex-transitive graphs, Cent. Eur. J. Math. 3 (2005), no. 2, 254–250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.

How to cite

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Baez, Karla. "Towards a geometric theory for left loops." Commentationes Mathematicae Universitatis Carolinae 55.3 (2014): 315-323. <http://eudml.org/doc/261874>.

@article{Baez2014,
abstract = {In [Mwambene E., Multiples of left loops and vertex-transitive graphs, Cent. Eur. J. Math. 3 (2005), no. 2, 254–250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.},
author = {Baez, Karla},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {left loops; Cayley graphs; rate of growth; hyperbolicity; left loops; Cayley graphs; growth rates; hyperbolicity},
language = {eng},
number = {3},
pages = {315-323},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Towards a geometric theory for left loops},
url = {http://eudml.org/doc/261874},
volume = {55},
year = {2014},
}

TY - JOUR
AU - Baez, Karla
TI - Towards a geometric theory for left loops
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2014
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 55
IS - 3
SP - 315
EP - 323
AB - In [Mwambene E., Multiples of left loops and vertex-transitive graphs, Cent. Eur. J. Math. 3 (2005), no. 2, 254–250] it was proved that every vertex-transitive graph is the Cayley graph of a left loop with respect to a quasi-associative Cayley set. We use this result to show that Cayley graphs of left loops with respect to such sets have some properties in common with Cayley graphs of groups which can be used to study a geometric theory for left loops in analogy to that for groups.
LA - eng
KW - left loops; Cayley graphs; rate of growth; hyperbolicity; left loops; Cayley graphs; growth rates; hyperbolicity
UR - http://eudml.org/doc/261874
ER -

References

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