Higher identities for the ternary commutator
نویسندگان
چکیده
منابع مشابه
Higher Identities for the Ternary Commutator
We use computer algebra to study polynomial identities for the trilinear operation [a, b, c] = abc − acb − bac + bca + cab − cba in the free associative algebra. It is known that [a, b, c] satisfies the alternating property in degree 3, no new identities in degree 5, a multilinear identity in degree 7 which alternates in 6 arguments, and no new identities in degree 9. We use the representation ...
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If n is any positive integer, then an n-algebra is a vector space A over a field F together with a linear map v : Amn a A, where Amn denotes the n-fold tensor power of A. In the case n s 3 we say that A is a ternary Ž . algebra or triple system . To simplify notation, we write a a ??? a 1 2 n Ž . Ž . instead of v a m a m ??? m a for a g A 1 F i F n . 1 2 n i Given the n-algebra A, we can define...
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and Applied Analysis 3 Step 1. Let F {a} be singleton. Then, there are u ∈ U and v ∈ V such that ‖uv‖ < M, and ‖ u, v, a − a‖ < M 1 . 2.2 Letting w uv ◦ uv, then ‖ uv ◦ uv, a − a‖ ‖ u, v, u, v, a − a − u, v, a − a ‖ < . 2.3 Step 2. Let F {a1, a2}. There is a u1, v1 ∈ U × V such that ‖ u1, v1, a1 − a1‖ < / 1 M , and for u1, v1, a2 − a2 ∈ A there is a u2, v2 ∈ U × V such that ‖ u2, v2, u1, v1, a2...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and Theoretical
سال: 2012
ISSN: 1751-8113,1751-8121
DOI: 10.1088/1751-8113/45/50/505201