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removed a deprecate tag and added one more tag instead - as discussed here: https://chat.stackexchange.com/transcript/10243/2020/2/5
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Martin Sleziak
Martin Sleziak
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Language editing; added top-level tag.
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Stefan Kohl ♦
Stefan Kohl ♦
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How can the Cayley-table table for the elements of basis of a Cayley-Dickson algebra be summarized in an algebraic expression?

One would be able to construct a Cayley table that has all $e_i$ elements of the basis of algebra $A$ where $0<i<\dim A$ such that $e_0=1$ and, $e_1=i$ and, $e_2=j$ and so on. I'm looking for an algebraic expression of the table for an algebra with dimensions Nof dimension $N$, such thatwhich enables me to getfind the result ofproduct $e_ie_j$ without looking at the table. Does such an expression exist?

P.S. The cayleyCayley tables for Quaternionsquaternions, Octonionsoctonions and Sedonionssedonions can be viewed infound in Wikipedia.

How can the Cayley-table for the elements of basis of a Cayley-Dickson algebra be summarized in an algebraic expression?

One would be able to construct a Cayley table that has all $e_i$ elements of the basis of algebra $A$ where $0<i<\dim A$ such that $e_0=1$ and $e_1=i$ and $e_2=j$ and so on. I'm looking for an algebraic expression of the table for an algebra with dimensions N, such that enables me to get the result of $e_ie_j$ without looking at the table. Does such an expression exist?

P.S. The cayley tables for Quaternions, Octonions and Sedonions can be viewed in Wikipedia.

How can the Cayley table for the elements of basis of a Cayley-Dickson algebra be summarized in an algebraic expression?

One would be able to construct a Cayley table that has all $e_i$ elements of the basis of algebra $A$ where $0<i<\dim A$ such that $e_0=1$, $e_1=i$, $e_2=j$ and so on. I'm looking for an algebraic expression of the table for an algebra of dimension $N$, which enables me to find the product $e_ie_j$ without looking at the table. Does such an expression exist?

P.S. The Cayley tables for quaternions, octonions and sedonions can be found in Wikipedia.

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user272651
user272651
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How can the Cayley-table for the elements of basis of a Cayley-Dickson algebra be summarized in an algebraic expression?

One would be able to construct a Cayley table that has all $e_i$ elements of the basis of algebra $A$ where $0<i<\dim A$ such that $e_0=1$ and $e_1=i$ and $e_2=j$ and so on. I'm looking for an algebraic expression of the table for an algebra with dimensions N, such that enables me to get the result of $e_ie_j$ without looking at the table. Does such an expression exist?

P.S. The cayley tables for Quaternions, Octonions and Sedonions can be viewed in Wikipedia.