Displaying similar documents to “On the existence of a Haar measure in topological IP-loops”

Algebraic aspects of web geometry

Maks A. Akivis, Vladislav V. Goldberg (2000)

Commentationes Mathematicae Universitatis Carolinae

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Algebraic aspects of web geometry, namely its connections with the quasigroup and loop theory, the theory of local differential quasigroups and loops, and the theory of local algebras are discussed.

Classification results in quasigroup and loop theory via a combination of automated reasoning tools

Volker Sorge, Simon Colton, Roy McCasland, Andreas Meier (2008)

Commentationes Mathematicae Universitatis Carolinae

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We present some novel classification results in quasigroup and loop theory. For quasigroups up to size 5 and loops up to size 7, we describe a unique property which determines the isomorphism (and in the case of loops, the isotopism) class for any example. These invariant properties were generated using a variety of automated techniques --- including machine learning and computer algebra --- which we present here. Moreover, each result has been automatically verified, again using a variety...

Bol loops with a large left nucleus

Orin Chein, Edgar G. Goodaire (2008)

Commentationes Mathematicae Universitatis Carolinae

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Possession of a unique nonidentity commutator/associator is a property which dominates the theory of loops whose loop rings, while not associative, nevertheless satisfy an ``interesting'' identity. Indeed, until now, with the exception of some ad hoc examples, the only known class of Bol loops whose loop rings satisfy the right Bol identity have this property. In this paper, we identify another class of loops whose loop rings are ``strongly right alternative'' and present various constructions...