Today was the first day of the Third Mile High Conference on Nonassociative Mathematics at University of Denver. Looks like a good group of people, only a few of whom I know. Yay for making connections.
Had lunch with Aleš Drápal today; I don't believe that we'd ever actually met before, though he immediately knew who I was, as I expected. The world is still small.
Neither he nor I are actively working on LD-related research at the moment, though finite LDs form nice test examples for computational packages; he mentioned that he has some unpublished theorems relating to the "levels" of homomorphisms between Laver tables. He also mentioned a direction of possible research that he had mostly abandoned, but where there might be results of manageable difficulty for a person or collaboration with the right crossover knowledge:
Let A=⟨A;∗ be a LD-groupoid (probably finite and monogenerated). It is known that in some cases, such as when A is a Laver Table, we can define an associative composition ∘ on A satisfying
To future me, who wants to play around with this problem: start with Aleš' paper in Semigroup Forum 51, "On the semigroup structure of cyclic left distributive algebras".
Had lunch with Aleš Drápal today; I don't believe that we'd ever actually met before, though he immediately knew who I was, as I expected. The world is still small.
Neither he nor I are actively working on LD-related research at the moment, though finite LDs form nice test examples for computational packages; he mentioned that he has some unpublished theorems relating to the "levels" of homomorphisms between Laver tables. He also mentioned a direction of possible research that he had mostly abandoned, but where there might be results of manageable difficulty for a person or collaboration with the right crossover knowledge:
Let A=⟨A;∗ be a LD-groupoid (probably finite and monogenerated). It is known that in some cases, such as when A is a Laver Table, we can define an associative composition ∘ on A satisfying
- (a∘b)∗c=a∗(b∗c)
- a∘b=(a∗b)∘a
- a∗(b∘c)=(a∗b)∘(a∗c)
To future me, who wants to play around with this problem: start with Aleš' paper in Semigroup Forum 51, "On the semigroup structure of cyclic left distributive algebras".
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