Given an alternative algebra A, is the algebra generated by two commutative, associative subalgebras B and C always associative?

Asked Oct 26 '23 at 17:56

Active Oct 26 '23 at 18:03

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The algebras are over a field.

The answer to the question is yes when B and C are generated by 1 element each. Over the octonions, the answer to the question is then yes. What about in general?

edited Oct 26 '23 at 18:03

asked Oct 26 '23 at 17:56

wlad

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Given an alternative algebra A, is the algebra generated by two commutative, associative subalgebras B and C always associative?

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