Applications for quasi-groups and loops outside of cryptography
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I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually get used for anything. Indeed what I find argues that its very hard to find any use for loops at all in physics or science.
I'm looking for any non-exotic applications of quasigroups or loops, the less exotic the better. I am aware that there is an attempt to formulate a Theory of Everything using octionions, a loop, but I'd say that's pretty much as exotic as it comes. The general question might be phrased "If a person did not already want to study quasigroups and loops, what reason might cause them to want to start said study?" Something to parallel how groups capture the concept of symmetry, which is easily applied in many cases, how monoids can be used for parallelizing operations like MapReduce or capture information in strong typed systems, or how inverse semigroups can be used to reason about partial symmetry.
applications
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
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add a comment |
$begingroup$
I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually get used for anything. Indeed what I find argues that its very hard to find any use for loops at all in physics or science.
I'm looking for any non-exotic applications of quasigroups or loops, the less exotic the better. I am aware that there is an attempt to formulate a Theory of Everything using octionions, a loop, but I'd say that's pretty much as exotic as it comes. The general question might be phrased "If a person did not already want to study quasigroups and loops, what reason might cause them to want to start said study?" Something to parallel how groups capture the concept of symmetry, which is easily applied in many cases, how monoids can be used for parallelizing operations like MapReduce or capture information in strong typed systems, or how inverse semigroups can be used to reason about partial symmetry.
applications
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
$endgroup$
add a comment |
$begingroup$
I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually get used for anything. Indeed what I find argues that its very hard to find any use for loops at all in physics or science.
I'm looking for any non-exotic applications of quasigroups or loops, the less exotic the better. I am aware that there is an attempt to formulate a Theory of Everything using octionions, a loop, but I'd say that's pretty much as exotic as it comes. The general question might be phrased "If a person did not already want to study quasigroups and loops, what reason might cause them to want to start said study?" Something to parallel how groups capture the concept of symmetry, which is easily applied in many cases, how monoids can be used for parallelizing operations like MapReduce or capture information in strong typed systems, or how inverse semigroups can be used to reason about partial symmetry.
applications
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
$endgroup$
I've been studying the group-like structures lately. Loops (and more generally quasigroups) seem strange in that they are defined, and we've studied their properties, but they don't seem to actually get used for anything. Indeed what I find argues that its very hard to find any use for loops at all in physics or science.
I'm looking for any non-exotic applications of quasigroups or loops, the less exotic the better. I am aware that there is an attempt to formulate a Theory of Everything using octionions, a loop, but I'd say that's pretty much as exotic as it comes. The general question might be phrased "If a person did not already want to study quasigroups and loops, what reason might cause them to want to start said study?" Something to parallel how groups capture the concept of symmetry, which is easily applied in many cases, how monoids can be used for parallelizing operations like MapReduce or capture information in strong typed systems, or how inverse semigroups can be used to reason about partial symmetry.
applications
applications
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
asked Dec 7 '18 at 21:25
Cort AmmonCort Ammon
2,451716
2,451716
add a comment |
add a comment |
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