flexible algebra
A non-associative algebra is flexible if for all , where is the associator on . In other words, we have for all . Any associative algebra is clearly flexible. Furthermore, any alternative algebra with characteristic is flexible.
Given an element in a flexible algebra , define the left power of iteratively as follows:
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1.
,
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2.
.
Similarly, we can define the right power of as:
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1.
,
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2.
.
Then, we can show that for all positive integers . As a result, in a flexible algebra, one can define the (multiplicative) power of an element as unambiguously.
Title | flexible algebra |
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Canonical name | FlexibleAlgebra |
Date of creation | 2013-03-22 14:43:30 |
Last modified on | 2013-03-22 14:43:30 |
Owner | CWoo (3771) |
Last modified by | CWoo (3771) |
Numerical id | 11 |
Author | CWoo (3771) |
Entry type | Definition |
Classification | msc 17A20 |
Related topic | Associator |
Related topic | AlternativeAlgebra |
Defines | left power |
Defines | right power |
Defines | flexible |