Questions tagged [nonassociative-algebras]

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Does there exist an anti-associative structure on a set with three elements?

A friend and I discussed whether there exist operations that are never associative in the sense that $$x(yz)\neq (xy)z$$ for all x, y, z and after pondering I found a simple example on a set with 2 ...
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Subalgebras of the Real Octonions under Multiplication

I am interested to know what the subalgebras of the octonions look like. I tried searching for it but to no avail. What did show up was "Subalgebras of the Split Octonions," which was quite nice. Yet, ...
21 views

Jordan Identity over $char\neq2$ implies power-associativity?

Let $A$ be non-comutative Algebra over a field of characteristic not 2 that satisfies $(xx)(xy)=x(y(xx))$. Can we say that $A$ is power-associative? My attempt: I'm trying to disprove the claim for ...
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How may one compute the proportion of isomorphisms among the total quantity of different combinations of element sequences and associative groupings?

If I have n elements in each possible sequence with each possible Tamari lattice grouping of those sequences with respect to a non-associative commutative operation, how may one compute the proportion ...
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What is the preferred convention for denoting Tamari lattice groupings?

Is there a common method or standard for denoting Tamari lattice/associative groupings with a character length less than that of the sum of the quantity of elements and parenthesis to be denoted? I ...
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A question about the Dendriform algebra

Dendriform algebra is a well-known non-associative algebra defined by Loday and Ronco. More precisely, A Dendriform algebra is a $k$-module $D$ together with two binary operations $\{\prec, \succ\}$...
I am trying to prove it but not getting any clue how to start it! $$a*b=b*a=e,$$ $$a*c=c*a=e$$ How to show $b=c$?
I'm reading Humphreys' Introduction to Lie Algebras and Representation Theory and I have a question about Corollary 14.1, which reads: Humphreys Corollary 14.1. Let $L$ be a semisimple Lie algebra,...